AnswersHCISD-Mathematical Models with Applications B-CR SUMMEREquations of Proportional Relationships

Equations of Proportional Relationships Answers

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Peter uses the equation to model the number of miles that he has walked in x hours. Which statement is true about the proportional relationship that is modeled by Peter’s equation?

Question illustration
A
Peter walks at a rate of miles per hour.
Option A
B
Peter walks at a rate of 4 miles per hour.
C
Peter walks at a rate of miles per hour.
Option C
D
Peter walks at a rate of 13 miles per hour.
2
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What is the constant of proportionality in the equation?

Question illustration
A
0
B
1
C
4
D
5
3

Which equation represents a proportional relationship that has a constant of proportionality equal to 2?

A
y = x + 2
Option A
B
y = StartFraction x over 2 EndFraction
Option B
C
y = 2 x
Option C
D
y = 2
Option D
4

Which equation represents a proportional relationship that has a constant of proportionality equal to ?

Question illustration
A
StartFraction y over x EndFraction = StartFraction 7 over 10 EndFraction
Option A
B
StartFraction y over x EndFraction = StartFraction 1 over 7 EndFraction
Option B
C
x y = StartFraction 7 over 10 EndFraction
Option C
D
x y = StartFraction 1 over 7 EndFraction
Option D
5

The fine schedule for overdue books at the county library is modeled by the values in the table.Library Fines for Overdue BooksDays overdueAmount of fine00 ¢25 ¢410 ¢615 ¢820 ¢1025 ¢Which equation best models the fine schedule for overdue books?

A
, where x is the cost in cents for a book that is y days overdue
Option A
B
, where y is the cost in cents for a book that is x days overdue
Option B
C
, where x is the cost in cents for a book that is y days overdue
Option C
D
, where y is the cost in cents for a book that is x days overdue
Option D
6

Which equation represents a proportional relationship that has a constant of proportionality equal to ?

Question illustration
A
y = x minus one-fifth
Option A
B
y = x + one-fifth
Option B
C
y = one-fifth x
Option C
D
y = 5 x
Option D
7

Rita is developing an equation that will represent the same proportional relationship as the graph.How will the ordered pair help her when she finds the equation?

Question illustration
A
The product of the coordinates will be a constant term in the equation.
B
The quotient of the coordinates will be a constant term in the equation.
C
The product of the coordinates will be a coefficient in the equation.
D
The quotient of the coordinates will be a coefficient in the equation.
8

The Hernandez family orders 3 large pizzas. They cut the pizzas so that each pizza has the same number of slices, giving them a total of 24 slices.The Wilson family also orders several large pizzas from the same pizza restaurant. They also cut the pizzas so that all their pizzas have the same number of slices. For the Wilson family, the equation y = 10x represents the relationship, where x represents the number of pizzas and y represents the number of total slices.Which statements best describe the pizzas bought by the Hernandez and Wilson families? Select two options.

A
For the Hernandez family, the equation y = 3x represents the relationship between the number of slices and number of pizzas, where x represents the number of pizzas and y represents the number of total slices.
B
For each family, a graph of the relationship between number of pizzas, x, and number of slices, y, goes through the point (0, 0) and is a straight line.
C
The Hernandez family’s slices are smaller than the Wilson family’s slices.
D
If the Wilson family ordered 3 large pizzas from the same restaurant as the Hernandez family, they would have more slices than the Hernandez family after each family cut their pizzas into slices.
E
The constant of proportionality is 10 for the Wilson family, but cannot be determined for the Hernandez family.
9

Joylin is writing an equation to model the proportional relationship between y, the total cost in dollars of downloading videos from a website, and x, the number of videos downloaded. She knows that the total cost to download 3 videos was $12. Her work to find the equation is shown below.Joylin’s WorkStep 1Step 2 Where did Joylin make her first error?

Question illustration
A
Joylin divided 3 and 12 instead of multiplying the two numbers.
B
Joylin computed the decimal equivalent of incorrectly.
Option B
C
Joylin used 0.25 as the coefficient of x instead of a product of x and y.
D
Joylin switched the numerator and the denominator when she found k.
10

What is the constant of proportionality in the equation ?

Question illustration
A
StartFraction 2 over 9 EndFraction
Option A
B
2
C
StartFraction 9 over 2 EndFraction
Option C
D
9

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