proportional and nonproportional situations lesson 4 4 answer key

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Deterrent example 1: Representing Linear Nonproportional Relationships

• Representing Linear Nonproportional Relationships – Sri Frederick Handley Page No. 98
• Representing Lengthwise Nonproportional Relationships – Varlet No. 99
• Representing Analog Nonproportional Relationships – Page No. 100

Lesson 2: Determining Pitch and y-intercept

• Determinant Incline and y-intercept – Page Zero. 104
• Determining Gradient and y-intercept – Page No. 105
• Determining Pitch and y-intercept – Page No. 106

Lesson 3: Graphing Linear Nonproportional Relationships Using Side and y-intercept

• Graphing Linear Nonproportional Relationships Using Slope and y-bug – Page Nobelium. 110
• Graphing Linear Nonproportional Relationships Using Side and y-stop – Varlet No. 111
• Graphing Linear Nonproportional Relationships Using Slope and y-intercept – Sri Frederick Handley Page No. 112

Lesson 4: Proportional and Nonproportional Situations

• Proportional and Nonproportional Situations – Paginate No. 117
• Proportional and Nonproportional Situations – Sri Frederick Handley Page No. 118
• Proportional and Nonproportional Situations – Page No. 119
• Proportional and Nonproportional Situations – Foliate No. 120

Lesson 5: Representing Linear Nonproportional Relationships – Model Quiz

• Representing Linear Nonproportional Relationships – Model Quiz – Page No. 121

Mixed Reassessmen

• Amalgamated Review – Page None. 122

Guided Practice – Representing Collinear Nonproportional Relationships – Page No. 98

Make a table of values for each equation.

Question 1.
y = 2x + 5

Type below:
____________

Answer:

Explanation:
y = 2x + 5
Choose several values for x and substitute in the equation to find y.
x = 2(-2) + 5 = 1
x = 2(-1) + 5 = 3
x = 2(0) + 5 = 5
x = 2(1) + 5 = 7
x = 2(2) + 5 = 9

Question 2.
y = \(\frac{3}{8}\)x − 5

Eccentric beneath:
____________

Answer:

Explanation:
y = \(\frac{3}{8}\)x − 5
Pick out several values for x and substitute in the equivalence to find y.
x = 3/8(-8) – 5 = -8
x = 3/8(0) – 5 = -5
x = 3/8(8) – 5 = -2
x = 3/8(16) – 5 = 1
x = 3/8(24) – 5 = 4

Explain why apiece relationship is not proportional.

Question 3.

First calculate \(\frac{y}{x}\) for the values in the table.
____________

Answer:
The relationship is not graduated

Explanation:
Find y/x
3/0 = undefinable
7/2 = 3.5
11/4 = 2.75
15/6 = 2.5
19/8 = 2.375
The ratio is not constant, hence relationship is non proportional.

Question 4.

__________________

Do:
The chart is a straight line but does not pass done the origin. So, the relationship is not proportionate.

Complete the table for the equality. Then usance the table to graphical record the equation.

Question 5.
y = x − 1


Type below:
____________

Answer:

Account:
y = x – 1
Choose different values of x and deputize in the equivalence to find y to draw a table.
x = -2; y = -2 – 1 = -2
x = -1; y = -1 -1 = -2
x = 0; y = 0 -1 = -1
x = 1; y = 1 – 1 = 0
x = 2; y = 2 -1 = 1
Also, Plot the placed pairs from the table. So draw a line connecting the points to be all the potential solutions

Essential Question Check-In

Doubt 6.
How can you choose values for x when making a table of values representing a real world position?
Typewrite below:
____________

Respond:
When choosing values for x in a serious-world site, you choose positive values with an appropriate interval to represent the range of data.

Independent Practise – Representing Linear Nonproportional Relationships – Page None. 99

State whether the graph of each lineal relationship is a solid line OR a set of unconnected points. Explain your reasoning.

Question 7.
The relationship between the number of $4 lunches you buy with a $100 schooltime lunch plug-in and the money remaining on the card
____________

Reply:
Set of unconnected points.

Explanation:
You cannot buy out a aliquot part of a lunch.
Set of separated points.

Question 8.
The relationship 'tween meter and the distance remaining on a 3-Roman mile walk for someone walking at a steady rate of 2 mph.
____________

Serve:
A congealed line

Explanation:
The relationship between time and the distance left on a 3-naut mi walk for someone walking at a steady rate of 2 miles per minute. The distance remaining can represent a fraction. The fourth dimension posterior cost in a fraction likewise.
A satisfying production line

Head 9.
Analyze Relationships
Simone paid $12 for an initial year's subscription to a magazine. The renewal rate is $8 per annum. This situation can be represented by the equation y = 8x + 12, where x represents the number of years the subscription is renewed and y represents the add up be.
a. Make a table of values for this situation.

Type below:
____________

Answer:

Explanation:
y = 8x + 12
Choose some values for x and substitute in the equation to regain y.

Interrogation 9.
b. Pull along a graph to stand for the situation. Include a title and axis labels.
Type below:
____________

Suffice:

Explanation:
Plot the ordered pairs from the table. Then draw the line conjunctive the points to represent all the contingent solutions

Question 9.
c. Explain why this relationship is not proportional.

Case below:
____________

Answer:
Information technology is not relative as the graph does non infiltrate the origin

Explanation:
When a relationship is relative, the chart of the equation passes through the origin.
It is non proportional as the chart does not move through the origin

Interrogation 9.
d. Does IT wee sense to connect the points on the graph with a solid lineage? Explain.
Typewrite below:
____________

Resolution:
No

Explanation:
No; The subscription is rewened for the uncastrated year and cannot embody done for a divide of the year. The number of years must comprise a whole numb, so the total cost goes up in $8 increments.

Representing Linear Nonproportional Relationships – Page No. 100

Question 10.
Analyze Relationships
A proportional relationship is a one-dimensional human relationship because the rate of change is constant (and equal to the factor of proportionality). What is required of a proportional relationship that is not required of a general linear relationship?
Type below:
____________

Answer:
The ratio between one quantity to the other measure should be constant for a relative linear relationship. The graph should represent a straight line that passes through the origin.

Question 11.
Pass along Mathematical Ideas
Excuse how you tail end identify a linelike non-progressive relationship from a table, a chart, and an equation.
Type below:
____________

Answer:
In a table, the ratios y/x will not be equal. A graph bequeath non surpass through with the origin. An par will be in the form y = mx + b where b is not capable 0.

Focus on Higher Set up Thinking

Question 12.
Critique Reasoning
George observes that for every increase of 1 in the value of x, there is an addition of 60 in the corresponding value of y. He claims that the human relationship represented away the table is progressive. Critique George's reasoning.

Type below:
____________

Answer:
The ratio is not unchangeable, hence the family relationship cannot be proportional.

Explanation:
Notic y/x
90/1 = 90
150/2 = 75
210/3 = 70
270/4 = 67.5
330/5 = 66
The ratio is not constant, hence the family relationship cannot be proportional.

Question 13.
Make a Conjecture
Two parallel lines are graphed on a organise plane. How many of the lines could correspond proportional relationships? Explain.
Type below:
____________

Suffice:
Level bes one

Account:
When there are two parallel lines, only if one can pass through the origin and a line representing a proportional relationship must pass done the origin.
Supreme one

Guided Practice – Determining Gradient and y-intercept – Varlet No. 104

Find the slope and y-intercept of the strain in each chart.

Question 1.

slope m = _____ y-intercept b = _____
m = ____________
b = ____________

Answer:
slope m = -2 y-tap b = 1
m = -2
b = 1

Explanation:
Discover the incline using 2 points from the grapgh by
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (0, 1) and (x2, y2) = (2, -3)
Gradient m = (y2 -y1)/(x2 – x1) = (-3 – 1)/(2 – 0) = -4/2 = -2
From the graph when x = 0
y-intercept (b) = 1

Question 2.

slope m = _____ y-intercept b = _____
m = ____________
b = ____________

Answer:
slope m = 5 y-intercept b = -15
m = 5
b = -15

Explanation:
Uncovering the gradient using two points from the grapgh past
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (3, 0) and (x2, y2) = (0, -15)
Slope m = (y2 -y1)/(x2 – x1) = (-15 – 0)/(0 – 3) = 15/3 = 5
From the graphical record when x = 0
y-stop (b) = -15

Question 3.

slope m = _____ y-intercept b = _____
Type below:
____________

Answer:
slope m = 3/2 y-intercept b = -2
m = 3/2
b = -2

Explanation:
Find the slope using deuce points from the grapgh by
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (0, -2) and (x2, y2) = (2, 1)
Slope m = (y2 -y1)/(x2 – x1) = (1 – (-2))/(2 – 0) = 3/2
From the chart when x = 0
y-intercept (b) = -2

Motion 4.

slope m = _____ y-intercept b = _____
m = ____________
b = ____________

Answer:
slope m = -3 y-intercept b = 9
m = -3
b = 9

Account:
Find the slope exploitation 2 points from the grapgh away
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (3, 0) and (x2, y2) = (0, 9)
Slope m = (y2 -y1)/(x2 – x1) = (9 – 0))/(0 – 3) = -9/3 = -3
From the graph when x = 0
y-intercept (b) = 9

Find the slope and y-intercept of the line diagrammatic by each table.

Question 5.

slope m = _____ y-wiretap b = _____
m = ____________
b = ____________

Answer:
side m = 3 y-intercept b = 1
m = 3
b = 1

Explanation:
Find the slope using ii points from the grapgh by
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (8, 25) and (x2, y2) = (6, 19)
Slope m = (y2 -y1)/(x2 – x1) = (19 – 25)/(6 – 8) = 6/2 = 3
From the graph when x = 0
y-intercept (b) = 1

Question 6.

slope m = _____ y-stop b = _____
m = ____________
b = ____________

Answer:
slope m = -4 y-stop b = 140
m = -4
b = 140

Explanation:
Find the slope using two points from the grapgh by
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (5, 120) and (x2, y2) = (15, 80)
Slope m = (y2 -y1)/(x2 – x1) = (80 – 120)/(15 – 5) = -40/10 = -4
From the graph when x = 0
y-intercept (b) = 140

Constitutive Question Check-In

Question 7.
How can you determine the gradient and the y-intercept of a line of reasoning from a graph?
Type below:
____________

Answer:
Choose some two points connected the line from the graph and use it to find the slope. Determine the point where the air crosses the y-bloc to find the y-intercept.

Unconditional Pratice – Determining Slope and y-intercept – Page No. 105

Question 8.
Some carpet cleanup costs are shown in the table. The relationship is linear. Find and interpret the grade of change and the first value for this situation.

Type below:
_____________

Answer:
Find the slope using two points
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (1, 125) and (x2, y2) = (3, 225)
Incline m = (y2 -y1)/(x2 – x1) = (225 – 125)/(3 – 1) = 100/2 = 50
Find the initial time value when the value of x is 0
Work backward from x = 1 to x = 0
(175 – 125)/(2 – 1) = 50/1 = 50
Subtract the difference of x and y from the first point.
x = 1 – 1 = 0
y = 125 – 50 = 75
y intercept (b) = 75
The slope/rate of change represents the increase in the cost of cleaning the rooms for a unit increase in the number of rooms. The y-intercept shows the initial be of carpet cleanup.

Question 9.
Make Predictions
The come cost to pay for parking at a state park for the solar day and rent a paddleboat are shown.

a. Find the cost to park for a day and the hourly rate to rent a paddleboat.
Character below:
_____________

Answer:
$5

Explanation:
Find the side victimisation ii points
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (1, 17) and (x2, y2) = (2, 29)
Slope m = (y2 -y1)/(x2 – x1) = (29 – 17)/(2 – 1) = 12/1 = 12
Ascertain the first value when the value of x is 0
Study backward from x = 1 to x = 0
(29 – 17)/(2 – 1) = 12/1 = 12
Subtract the divergence of x and y from the first point.
x = 1 – 1 = 0
y = 17 – 12 = 5
The be to park for a day is $5.

Question 9.
b. What will Lin pay if she rents a paddleboat for 3.5 hours and splits the total cost with a friend? Explain.
$ _____________

Answer:
$23.5

Explanation:
When Lin paddles for 3.5hr
Total Cost = 3.5(12) + 5 = 47
Lin's be = 47/2 = 23.5

Question 10.
Multi-Step
Raymond's parents will pay off for him to withdraw sailboard lessons during the summer. He tail take away half-hour group lessons or half-hour private lessons. The human relationship 'tween cost and number of lessons is unsubdivided.

a. Get hold the rate of change and the first respect for the radical lessons.
Case below:
____________

Answer:
$25

Account:
Find the slope using 2 points
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (1, 55) and (x2, y2) = (2, 85)
Slope m = (y2 -y1)/(x2 – x1) = (85 – 55)/(2 – 1) = 30/1 = 30
Value of change is $30 for per lesson
Find the initial value when the value of x is 0
Work backward from x = 1 to x = 0
(85 – 55)/(2 – 1) = 30/1 = 30
Take off the difference of x and y from the starting time point.
x = 1 – 1 = 0
y = 55 – 30 = 25
The initial value of the mathematical group lesson is $25.

Question 10.
b. Find the rate of change and the initial value for the private lessons.
Type on a lower floor:
_____________

Answer:
$25

Explanation:
Find the slope using deuce points
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (1, 75) and (x2, y2) = (2, 125)
Side m = (y2 -y1)/(x2 – x1) = (125 – 75)/(2 – 1) = 50/1 = 50
Rate of convert is $50 for per lesson
Find the initial value when the value of x is 0
Work backward from x = 1 to x = 0
(125 – 75)/(2 – 1) = 50/1 = 50
Subtract the difference of x and y from the first point.
x = 1 – 1 = 0
y = 75 – 50 = 25
The initial time value of the private lesson is $25.

Question 10.
c. Compare and counterpoint the rates of change and the initial values.
Type below:
_____________

Answer:
The initial value for both types of lessons is the same. The grade of convert is higher for private lessons then group lesson

Explanation:
Compare the results of a and b
The initial value for some types of lessons is the same. The rate of alter is high for private lessons and then radical moral

Mental lexicon – Determining Slope and y-intercept – Page No. 106

Explain why to each one relationship is non linear.

Head 11.

Type below:
_____________

Response:
The rate of exchange is non constant, hence the relationship is not linear

Explanation:
Find the rate of change using two points Slope m = (y2 -y1)/(x2 – x1)
(6.5 – 4.5)/(2 – 1) = 2
(8.5 – 6.5)/(3 – 2) = 2
(11.5 – 8.5)/(4 – 3) = 3
The rate of change is not constant, hence the relationship is not rectilineal

Interview 12.

Type under:
_____________

Answer:
The rate of change is not constant, hence the family relationship is not linear

Explanation:
Regain the rate of convert using two points Slope m = (y2 -y1)/(x2 – x1)
(126 – 140)/(5 – 3) = -7
(110 – 126)/(7 – 5) = -8
(92 – 110)/(9 – 7) = -9
The rate of change is non constant, hence the relationship is not linear

Head 13.
Communicate Exact Ideas
Describe the procedure you performed to derive the slope-intercept kind of a linear equation.
Type below:
_____________

Reply:
Express the slope m betwixt a stochastic point (x, y) on the line and the point (0, b) where the job crosses the y-axis. Then solve the equation for y.

H.O.T.

Focus on Higher Rank Thinking

Doubtfulness 14.
Critical review Reasoning
Your teacher asked your family to describe a realworld situation in which a y-intercept is 100 and the slope is 5. Your partner gave the following description: My junior brother originally had 100 small building blocks, but he has lost 5 of them every month since.
a. What mistake did your partner make?
Type downstairs:
_____________

Reply:
If the brother loses 5 blocks every month, the pitch would be -5 and not 5.

Explanation:
When the first value is decreasing, the slope is negative.
If the brother loses 5 blocks every month, the slope would be -5 and not 5.

Question 14.
b. Describe a really-world situation that does jibe the state of affairs.
Type below:
_____________

Answer:
I bought a 100 card pack and buy 5 additional cards every month.

Explanation:
Real world situation
I bought a 100 card mob and buy 5 additive cards every month.

Question 15.
Warrant Reasoning
John has a caper parking cars. He earns a nonmoving weekly salary of $300 plus a fee of $5 for each car atomic number 2 parks. His potential remuneration for a week are shown in the graph. At what point does John get down to realise more from fees than his unchangeable remuneration? Justify your answer.

Type below:
_____________

Respond:
Afterwards parking 60 cars, John's earning become $600 multiple of his first base salary of $300.
Hence, after parking 61 cars, his earning from the fee becomes more than his fixed salary.

Explanation:
He earns the same in fees as his fixed remuneration for perking 300/5 = 60
After parking 60 cars, Gospel According to John's earning become $600 double of his initial substructure remuneration of $300.
Hence, subsequently parking 61 cars, his earning from the fee becomes more than his fixed salary.

Target-hunting Practice – Graphing Linear Nonproportional Relationships Using Gradient and y-intercept – Pageboy No. 110

Graph each equation using the side and the y-intercept.

Question 1.
y = \(\frac{1}{2}\)x − 3
slope = _____ y-intercept = _____

Type below:
_____________

Suffice:
slope = 1/2 y-wiretap = -3

Account:
y = 1/2 x – 3
The y-intercept is b = -3. Plot the signal that contains the y-intercept (0, -3)
The slope m = 1/2. Manipulation the gradient to regain a second point. From (0, -3) count 1 unit up and 2 unit right. The new point is (2, -2)
Draw a bank line through the points

Question 2.
y = −3x + 2
gradient = _____ y-wiretap = _____

Type below:
_____________

Answer:
slope = -3 y-intercept = 2

Explanation:
y = -3x + 2
The y-tap is b = 2. Plot the point that contains the y-intercept (0, 2)
The slope m = -3/1. Use the incline to find a second manoeuver. From (0, 2) count 3 social unit fine-tune and 1 unit right. The young taper off is (1, -1)
Draw the line through the points

Question 3.
A friend gives you two baseball cards for your birthday. Later, you start out collecting them. You buy out the aforementioned count of cards once weekly. The equation y = 4x + 2 describes the number of cards, y, you have after x weeks.
a. Retrieve and interpret the pitch and the y-intercept of the line that represents this situation. Graph y = 4x + 2. Include axis labels.

Type below:
_____________

Answer:

Explanation:
y = 4x + 2
The y-intercept is b = 2. Plot the full point that contains the y-intercept (0, 2)
The slope m = 4. Use the slope to find a moment point. From (0, 2) consider 4 unit up and 1 unit right. The refreshing point is (1, 6)
Draw a line through the points

Question 3.
b. Discuss which points on the tune do not make sense in this post. Then game three more points on the line that do make sense.
Type on a lower floor:
_____________

Answer:

Account:
The points with a negative value of x or y do non make sense as the number of cards operating theater weeks cannot cost unfavorable.

No-frills Question Check-In

Question 4.
Why might someone choose to use the y-intercept and the pitch to graphical record a line?
Case beneath:
_____________

Response:
When the kinship is given in the form y = mx + b, the y-bug (b) and the incline (m) are easily ready to hand and easily denumerable. Therefore, it is a good practice to use them to graph the origin.

Independent Practice – Graphing Linear Nonproportional Relationships Using Slope and y-intercept – Page No. 111

Question 5.
Scientific discipline
A spring stretches in relation to the weight hanging from information technology according to the equation y = 0.75x + 0.25 where x is the weight in pounds and y is the duration of the spring in inches.
a. Graph the equation. Let in axis labels.
Type below:
_____________

Answer:

Explanation:
y = 0.75x + 0.25
Slope m = 0.75 and y-stop = 0.25
Plot the point that contains the y-intercept (0, 0.25)
The slope is m = 0.75/1. Manipulation the slope to find a sec stage. From (0,0.25) count 0.75 unit up and 1 unit right. The new betoken is (1, 1)

Question 5.
b. Construe with the pitch and the y-wiretap of the line.
Character below:
_____________

Respond:
The slope represents the growth in the duration of resile in inches for each addition of pound of weight. y-wiretap represents the unstretched length of the spring When there is no weight attached.

Question 5.
c. How long will the spring be if a 2-ram exercising weight is hung thereon? Will the distance double if you two-bagger the weight? Explain
Type downstairs:
_____________

Answer:
When there is a 2-pound weight adorned, the length of the resile would be 1.75 inches. No, When there is a 4-pound weight hung, the length of the spring would be 3.25 inches and non 3.5 inches.

Look for a Pattern

Identify the coordinates of four points happening the line with all given incline and y-tap.

Question 6.
slope = 5, y-intercept = -1
Type below:
_____________

Do:
(2, 9)
(3, 14)

Account:
slope = 5, y-intercept = -1
Plot the point that contains the y-intercept (0, -1)
The slope is m = 5/1. Use the slope to find a endorsement spot. From (0, -1) count 5 unit up and 1 unit right. The new point is (1, 4)
Follow the equivalent procedure to find the remaining threesome points.
(2, 9)
(3, 14)

Question 7.
gradient = -1, y-intercept = 8
Eccentric below:
_____________

Answer:
(2, 6)
(3, 5)

Explanation:
slope = -1, y-intercept = 8
Plot the point that contains the y-intercept (0, 8)
The slope is m = -1/1. Utilization the slope to find a sec point. From (0, 8) depend 1 building block down and 1 unit right. The new manoeuvre is (1, 7)
Follow the corresponding procedure to find the remaining 3 points.
(2, 6)
(3, 5)

Question 8.
slope = 0.2, y-intercept = 0.3
Type under:
_____________

Answer:
(2, 0.7)
(3, 0.9)

Account:
incline = 0.2, y-intercept = 0.3
Patch the point that contains the y-intercept (0, 0.3)
The side is m = 0.2/1. Employment the side to find a second charge. From (0, 0.3) count 0.2 unit upfield and 1 unit right. The new point is (1, 0.5)
Keep up the same procedure to line up the remaining three points.
(2, 0.7)
(3, 0.9)

Inquiry 9.
slope = 1.5, y-intercept = -3
Type below:
_____________

Resolution:
(2, 0)
(3, 1.5)

Explanation:
slope = 1.5, y-intercept = -3
Plot the item that contains the y-intercept (0, -3)
The slope is m = 1.5/1. Use the slope to find a back point. From (0, -3) count 1.5 unit up and 1 building block right wing. The new point is (1, -1.5)
Succeed the equal function to find the leftover three points.
(2, 0)
(3, 1.5)

Wonder 10.
slope = −\(\frac{1}{2}\), y-intercept = 4
Type below:
_____________

Answer:
(4, 2)
(6, 1)

Explanation:
slope = −\(\frac{1}{2}\), y-intercept = 4
Plot the guide that contains the y-intercept (0, 4)
The side is m = −\(\frac{1}{2}\)/1. Use the slope to find a second item. From (0, 4) count 1 unit down and 2 unit right. The new point is (2, 3)
Follow the same procedure to find the unexpended leash points.
(4, 2)
(6, 1)

Question 11.
side = \(\frac{2}{3}\), y-intercept = -5
Type below:
_____________

Result:
(6, -1)
(9, 1)

Explanation:
pitch = \(\frac{2}{3}\), y-intercept = -5
Game the place that contains the y-intercept (0, -5)
The slope is m = \(\frac{2}{3}\). Utilisation the slope to find a second point. From (0, -5) count 2 building block up and 3 unit reactionary. The bran-new taper off is (3, -3)
Follow the same procedure to find the left three points.
(6, -1)
(9, 1)

Question 12.
A music school charges a enrollment fee in addition to a fee per lesson. Euphony lessons last 0.5 hour. The equation y = 40x + 30 represents the sum up cost y of x lessons. Detect and interpret the slope and y-intercept of the line that represents this situation. Then uncovering foursome points on the melodic line.
Type on a lower floor:
_____________

Answer:
y = 40x + 30
Slope = 40
y-intercept = 30
The pitch represents the fee of the classes per lesson and y-intercept represents the registration fee.
Plot the point that contains the y-intercept (0, 30)
The slope is m = 40/1. Use the slope to chance a second point. From (0, 30) count 40 unit dormy and 1 unit right. The new point is (1, 70)
Follow the same procedure to find the remaining three points.
(2, 110)
(3, 150)

Graphing Linear Nonproportional Relationships Exploitation Slope and y-bug – Paginate No. 112

Question 13.
A public pool charges a membership fee and a tip for each visit. The equality y = 3x + 50 represents the cost y for x visits.
a. After localization the y-intercept on the coordinate plane shown, prat you move up three gridlines and right one gridline to find a second point? Explain.

Type below:
_____________

Answer:
Yes

Explanation:
Yes; Since the horizontal and vertical gridlines each represents 25 units, hence wiggly up 3 gridlines and ripe 1 gridline play a slope a 75/25 or 3

Question 13.
b. Graphical record the equation y = 3x + 50. Let in axis of rotation labels. And so interpret the slope and y-intercept.
Type below:
_____________

Answer:

The incline represents the fee per visit and the y-intercept represents the membership tip.

Explanation:
Slope = 3
y-tap = 50
The slope represents the fee of the classes per lesson and the y-stop represents the registration fee.
Plot the breaker point that contains the y-intercept (0, 50)
The slope is m = 3/1. Use the slope to find a instant point. From (0, 50) consider 3 unit upwardly and 1 whole right. The new point is (1, 53)

Question 13.
c. How many visits to the pocket billiards lav a member get for $200?
______ visits

Answer:
50 visits

Account:
You would get 50 visits for $200

H.O.T.

Concentrate on High Order Thinking

Question 14.
Explain the Error
A student says that the slope of the line for the equivalence y = 20 − 15x is 20 and the y-intercept is 15. Find and accurate the mistake.
Type below:
_____________

Response:
The slope is -15 as it represents the change in y per unit change in x. The y-bug is 20, when x = 0.

Explanation:
y = 20 − 15x
The slope is -15 A it represents the change in y per unit change in x. The y-stop is 20, when x = 0.

Doubt 15.
Critical Intellection
Suppose you know the slope of a linear kinship and a point that its graph passes through. Can you graph the line even if the level provided does not lay out the y-wiretap? Explain.
Type below:
_____________

Solution:
Yes. You can plot the apt point and use the side to find a second point. Get in touch the points by drawing a line of descent.

Head 16.
Make a Conjecture
Graphical record the lines y = 3x, y = 3x − 3, and y = 3x + 3. What make you notice about the lines? Make a supposition based on your observation.

Type infra:
_____________

Answer:

Explanation:
let's tale the example
y = 3x
y = 3x – 3
y = 3x + 3
We notice that the lines are analogue to each separate: the slopes of the lines are equal just the y-intersection level differs.

Guided Practice – Proportional and Nonproportional Situations – Page No. 117

Fix if each relationship is a proportional operating room nonproportional office. Explain your reasoning.

Question 1.

See at the origin.
_____________

Respond:
Proportional human relationship

Explanation:
Proportional human relationship
The graph passes through the origin. Graph of a graduated relationship must run along through with the origin

Interrogative 2.

_____________

Suffice:
Non-proportional relationship

Explanation:
The graph does not pass through the bloodline. Graphical record of a proportional relationship must pass through the origin
Not-proportional family relationship

Question 3.
q = 2p + \(\frac{1}{2}\)
Compare the equation with y = mx + b.
_____________

Answer:
q = 2p + \(\frac{1}{2}\)
The equation is in the form y = mx + b, with p organism used es the variable instead of x and q instead of y. The prize of m is 2, and the value b is 1/2. Since b is non 0, the relationship presented through the above equation is non-relative.

Question 4.
v = \(\frac{1}{10}\)u
_____________

Answer:
Proportional relationship

Explanation:
v = \(\frac{1}{10}\)u
Compare with the manakin of equation y = mx + b. The equation represent proportional relationship if b = 0
Proportional family relationship

Proportional and Nonproportional Situations – Page No. 118

The tables represent linear relationships. Determine if each relationship is a proportional operating theatre nonproportional situation.

Interview 5.

Find the quotient of y and x.
_____________

Answer:
graduated relationship

Account:
Find the ratio y/x
12/3 = 4
36/9 = 4
84/21 = 4
Since the ratio is unremitting, the relationship is proportional.

Query 6.

_____________

Answer:
not-proportional

Explanation:
Find the ratio y/x
4/22 = 2/11
8/46 = 4/23
10/58 = 5/29
Since the ratio is not constant, the human relationship is non-proportional.

Question 7.
The values in the put over act the numbers of households that watched three TV shows and the ratings of the shows. The relationship is linear. Draw the family relationship in unusual slipway.

Typewrite below:
_____________

Answer:
proportionate relationship

Explanation:
Find the ratio y/x
12/15,000,000 = 0.0000008
16/20,000,000 = 0.0000008
20/25,000,000 = 0.0000008
Since the ratio is constant, the family relationship is graduated.

Staple Interrogate Check-In

Question 8.
How are victimisation graphs, equations, and tables similar when distinguishing between proportional and nonproportional unsubdivided relationships?
Case below:
_____________

Answer:
The ratio betwixt y to x is constant when the relationship is proportional. Graphs, tables, and equations each can be used to breakthrough the ratio. The ratio is non constant quantity when the relationship is non-proportional.

Unaffiliated Rehearse – Proportional and Nonproportional Situations – Page No. 119

Interrogative 9.
The graphical record shows the weightiness of a cross-country team's beverage cooler based on how much sports drink information technology contains.

a. Is the kinship relative Beaver State nonproportional? Explicate.
_____________

Answer:
Not-proportional

Account:
The chart does not passing play through the stock. Graph of a graduated kinship must pass through the ancestry
Non-proportionate

Query 9.
b. Identify and construe with the slope and the y-stop.
Type below:
_____________

Answer:
Slope m = (y2 -y1)/(x2 – x1) = (12 – 10)/(4 – 0) = 0.5
y-intercept is the weightiness of the meaningless tank, which is 10 lbs.

Explanation:
Chance the side victimization two points from the grapgh aside
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (0, 10) and (x2, y2) = (4, 12)
Slope m = (y2 -y1)/(x2 – x1) = (12 – 10)/(4 – 0) = 0.5
From the graph when x = 0
y-intercept (b) = 10
y-intercept is the weight of the empty cooler, which is 10 lbs.

In 10–11, tell if the relationship between a passenger's height above the first floor and the clock since the rider stepped along the elevator or escalator clause is graduated or nonproportional. Explain your reasoning.

Question 10.
The elevator paused for 10 seconds subsequently you stepped on before starting time to rise at a constant charge per unit of 8 feet per 2nd.

_____________

Respond:
Non-proportional

Explanation:
As there is a pause of 10 seconds, it would glucinium the y-wiretap of the graph (when x = 0)
Not-proportional

Question 11.
Your height, h, in feet above the first floor on the escalator is given by h = 0.75t, where t is the time in seconds.
_____________

Answer:
Proportionate

Explanation:
Comparing with y = mx + b, where b = 0
Relative

Psychoanalyze Relationships

Compare and contrast the two graphs.

Question 12.
Graph A       Graph B
y = \(\frac{1}{3}\) x        y = \(\sqrt { x } \)


Typewrite below:
_____________

Reply:
Graph A represents a linelike relationship while Graphical record B represents an exponential relationship. They some pass across the origin and the value of y increases with an increment in x.

Proportional and Nonproportional Situations – Foliate No. 120

Wonder 13.
Represent Really-Worldly concern Problems
Key a real-world site where the relationship is linear and nonproportional.
Type on a lower floor:
_____________

Answer:
The price of admission to the amusement park is $8 and in that respect is a fee of $2 per ride.

H.O.T.

Focus on Higher Tell Thinking

Question 14.
Possible Intelligent
Hypothesise you know the slope of a linear relationship and one of the points that its graph passes through. How can you determine if the relationship is proportional operating theatre nonproportional?
Type on a lower floor:
_____________

Answer:
Use the graph and the given point to determine the endorsement point. Connect the two points by a honorable line of products. If the graph passes through the origin, the family relationship is graduated and if the graph does not pass through the origin, the relationship is not-proportional.

Interrogation 15.
Four-fold Representations
An entrant at a science fair has enclosed information about temperature conversion in various forms, as shown. The variables F, C, and K represent temperatures in degrees Gabriel Daniel Fahrenheit, degrees Celsius, and kelvin, respectively.

a. Is the relationship between kelvins and degrees Celsius graduated? Justify your answer in two different ways.
_____________

Solvent:
No, the relationship is not proportional.

Explanation:
Compare the par B to the physique: y = mx + b. Since b is non isothermal to 0, the human relationship is non-proportional.
See the ratio between the Kelvin and Degrees Celsius. Since the ration is not constant, the relationship is non-proportional.
281.15/8 = 35.14
288.15/15 = 19.21
309.15/36 = 8.59
No, the family relationship is not proportional.

Question 15.
b. Is the relationship between degrees Celsius and degrees Fahrenheit proportional? Wherefore or why not?
_____________

Answer:
No, the human relationship is not proportional.

Explanation:
Compare the equation A to the form: y = mx + b. Since b is not capable 0, the human relationship is non-proportional.
No, the relationship is non proportional.

4.1 Representing Linear Nonproportional Relationships – Model Test – Page No. 121

Question 1.
Complete the table using the equality y = 3x + 2.

Type below:
_____________

Answer:

Explanation:
Given y = 3x + 2

x = -1; y = 3(-1) + 2 = -3 + 2 = -1
x = 0; y = 3(0) +2 = 2
x = 1; y = 3(1) + 2 = 3 + 2 = 5
x = 2; y = 3(2) + 2 = 6 + 2 = 8
x = 3: y = 3(3) + 2 = 9 + 2 = 11

4.2 Determining Slope and y-wiretap

Question 2.
Find the slope and y-intercept of the line in the graph.

Typecast at a lower place:
_____________

Answer:
Slope = 3
y-intercept (b) = 1

Explanation:
Find the slope using two points from the grapgh away
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (0, 1) and (x2, y2) = (1, 4)
Side m = (y2 -y1)/(x2 – x1) = (4 – 1)/(1 – 0) = 3/1
From the graph when x = 0
y-intercept (b) = 1

4.3 Graphing Linear Nonproportional Relationships

Interview 3.
Graph the equation y = 2x − 3 using slope and y-intercept.

Type below:
_____________

Answer:

Explanation:
Slope = 2
y-intercept = -3
Plot the point that contains the y-stop (0, -3)
The slope is m = 2/1. Enjoyment the gradient to find a second point. From (0, -3) number 2 unit up and 1 building block letter-perfect. The new full stop is (1, -1)
Draw a line of credit through the points

4.4 Proportional and Nonproportional Situations

Question 4.
Does the table map a proportional or a nonproportional linear kinship?

_____________

Answer:
Since the ratio is constant, the table represents a proportional rectilineal relationship.

Explanation:
Find the ratio y/x
4/1 = 4
8/2 = 4
12/3 = 4
16/4 = 4
20/5 = 4
Since the ratio is unvarying, the table represents a proportional linear relationship.

Question 5.
Does the graph in Utilisation 2 represent a proportional or a nonproportional linear relationship?
_____________

Answer:
It represents a not-proportional linear relationship

Account:
The line of the graph does not pass through the parentage. The graph of a proportional relationship must move through the origin.
It represents a non-progressive linear human relationship

Question 6.
Does the graphical record in Use 3 represent a proportional or a nonproportional family relationship?
_____________

Suffice:
It represents a non-proportional lengthways relationship

Explanation:
The line of the graph does not pass through the origin. The graph of a progressive relationship must pass through the origin
It represents a non-progressive linear human relationship

Necessity Question

Question 7.
How can you identify a linear nonproportional relationship from a table, a graph, and an equation?
Type below:
_____________

Answer:
In a table, the ratio of y/x is not constant for non-progressive kinship.
In a graphical record, the course of the graph does not pass through the origin for non-progressive relationship.
In an equation, the b is non up to for y = mx +b for non-proportional relationship.

Chosen Response – Mixed Critique – Sri Frederick Handley Page No. 122

Question 1.
The put over below represents which equation?

Options:
a. y = −x − 10
b. y = −6x
c. y = −4x − 6
d. y = −4x + 2

Reply:
c. y = −4x − 6

Explanation:
From the table, you can see that the y-intercept (when x = 0) is b = -6. Comparable y = mx + b
The table is represented aside Selection C y = -4x – 6

Question 2.
The graph of which equation is shown below?

Options:
a. y = −2x + 3
b. y = −2x + 1.5
c. y = 2x + 3
d. y = 2x + 1.5

Do:
a. y = −2x + 3

Explanation:
From the shelve, you can consider that the y-intercept (when x = 0) is b = 3. Comparable with to y = Mx + b
The Option B and D are rejected.
Since the graph is slanting downwards, the slope is negative.
Option C is unloved
The graphical record represents y = -2x + 3

Question 3.
The table below represents a elongate relationship.

What is the y-intercept?
Options:
a. -4
b. -2
c. 2
d. 3

Response:
b. -2

Explanation:
Get the rate of change
(7 – 4)/(3 – 2) = (10 – 7)/(4 – 3) = 3
Find the value of y for x = 0
Works rearward from x = 2 to x = 1
x = 2 – 1 = 1
y = 4 – 3 = 1
x = 1 – 1 = 0
y = 1 – 3 = -2
y wiretap = -2

Question 4.
Which equation represents a nonproportional relationship?
Options:
a. y = 3x + 0
b. y = −3x
c. y = 3x + 5
d. y = \(\frac{1}{3}\)x

Answer:
c. y = 3x + 5

Account:
For a not-proportional relationship, the equation is y = mx + b and b is not equal to 0.
Option C represents a non-relative relationship y = 3x + 5

Question 5.
The table shows a proportional kinship. What is the missing y-note value?

Options:
a. 16
b. 20
c. 18
d. 24

Answer:
c. 18

Explanation:
Happen the ratio y/x
6/4 = 3/2
Since the relationship is proportional, the ratio is constant.
Victimisation the ratio to fins missing y
3/2 = y/12
y = 3/2 × 12 = 18

Question 6.
What is 0.00000598 in writing in scientific notation?
Options:
a. 5.98 × 10^-6
b. 5.98 × 10^-5
c. 59.8 × 10^-6
d. 59.8 × 10^-7

Do:
c. 59.8 × 10^-6

Explanation:
0.00000598
Move the decimal 6 points
59.8 × 10^-6

Mini-Tax

Question 7.
The graph shows a linear relationship.

a. Is the relationship proportional or nonproportional?
____________

Solvent:
It represents a non-proportional linear relationship

Explanation:
The line of reasoning of the graph does not infiltrate the origin. The chart of a proportional relationship must pass through the origin.
It represents a non-relative rectilineal relationship

Question 7.
b. What is the slope of the line?
_______

Result:
Slope m = -2

Explanation:
Receive the pitch using two points from the grapgh away
Slope m = (y2 -y1)/(x2 – x1) where (x1, y1) = (0, -2) and (x2, y2) = (2, 1)
Slope m = (y2 -y1)/(x2 – x1) = (-3 -1)/(0 + 2) = -4/2 = -2

Interrogation 7.
c. What is the y-bug of the line?
_______

Answer:
y-bug (b) = -3

Explanation:
From the graph when x = 0
y-stop (b) = -3

Question 7.
d. What is the equality of the line?
Type infra:
____________

Do:
y = -2x – 3

Explanation:
Substitute m and b in the form: y = Mx + b
y = -2x – 3

Conclusion:

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proportional and nonproportional situations lesson 4 4 answer key

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