AnswersHCISD-Mathematical Models with Applications B-CR SUMMERFinding a Constant of Proportionality

Identifying Proportional Relationships Answers

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Chad created a table that shows the ratio of his sports game cards.Chad’s CardsCard TypeOutfieldInfieldCatcherPitchersQuantity3412Next, Chad created the graph below showing possible ratios for Pitchers cards to Infield cards in his deck. Which of the following statements are true?

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A
Chad correctly included the points (1, 2) and (3, 6) because they maintain the same ratio of 1 Pitcher card to 2 Infield cards.
B
Chad should not have included the points (1, 2) and (3, 6) because these points do not maintain the same ratio between Pitchers and Infield cards.
C
Chad should have labeled the axes in the same order as the table to match the data presentation.
D
Chad needs to switch the order of each (x, y) value to show the decreasing values of the Pitchers cards.
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To celebrate ratios, Mrs. Johnson’s class will make pizzas. Julio is in charge of bringing in the sauce. There are 30 students in his class and each pizza serves 8.Pizza Sauce RecipePizzasPizza Sauce1 cup2 3 4 Which point should Julio use to determine the amount of pizza sauce he needs to bring?

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A
B
B
C
C
D
D
3

Which statement about the graph is true?

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A
The graph shows a proportional relationship because it is a line, and the difference between each point is the same.
B
The graph shows a proportional relationship because it is a line, and each x-value is a multiple of 2.
C
The graph does not show a proportional relationship because each point written as a ratio gives a different value.
D
The graph does not show a proportional relationship because a line that increases by 1 in the y-value cannot have a constant of proportionality.
4

Which statement about proportional relationships is false?

A
A proportional relationship must graph as a straight line.
B
A graph of a proportional relationship must pass through (0, 0).
C
Each point (or pair) in a proportional relationship must share the same ratio.
D
Each point (or pair) in a proportional relationship must share the same difference.
5

Sean has 4 science fiction books for every 3 sports books. Which graph represents his book collection?

A
On a coordinate plane, a graph titled Book Collection has science fiction on the x-axis and sports on the y-axis. Points (3, 4) and (6, 8) are plotted.
Option A
B
On a coordinate plane, a graph titled Book Collection has science fiction on the x-axis and sports on the y-axis. Points (3, 5) and (6, 9) are plotted.
Option B
C
On a coordinate plane, a graph titled Book Collection has science fiction on the x-axis and sports on the y-axis. Points (4, 3) and (8, 6) are plotted.
Option C
D
On a coordinate plane, a graph titled Book Collection has science fiction on the x-axis and sports on the y-axis. Points (3, 2) and (6, 4) are plotted.
Option D
6

Jonathon created a graph that shows the number of exercises he completes in his workout routine.Which statement summarizes his exercise routine?

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A
Jonathon does 3 crunches for every 2 push-ups.
B
Jonathon does 2 push-ups for every 3 crunches.
C
Jonathon does 2 push-ups for every 15 crunches.
D
Jonathon does 15 push-ups for every 2 crunches.
7

Robert can complete 10 inspections in 8 hours. Which represents the unit rate for the number of inspections he completes per hour?

A
0.8 of an inspection in 1 hour
B
4 inspections in 5 hours
C
1.25 inspections in 1 hour
D
5 inspections in 4 hours
8

Gregory noticed that his plant had grown 1.5 inches every two weeks since the day it sprouted. He created a table to show the plant’s weekly growth.Which statement about Gregory’s graph is true?

Question illustration
A
Gregory’s graph is correct because it shows 1.5 inches of growth for each week.
B
Gregory’s graph is incorrect because it shows 1.5 inches of growth for each week when it should show 3 inches for each week.
C
Gregory’s graph is incorrect because it shows 2 inches of growth for each week when it should show 0.75 inches of growth each week.
D
Gregory’s graph is correct because it shows 1.5 inches of growth every two weeks.
9

Sidaanth kept a chart of his savings. Which point represents this relationship?Sidaanth’s SavingsWeekSavings1$7.002$14.003$21.004$28.00

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A
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B
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D
10

What do the differences between the points (as shown on the graph) represent?

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A
is the unit rate because it compares the change in y-values to the change in x-values of the points on the graph.
Option A
B
is the unit rate because it compares the change in y-values to the change in x-values of the points on the graph.
Option B
C
can be used to find the unit rate if one divides 7 by 2 and compares the result to 1.
Option C
D
can be used to find the unit rate if one divides 2 by 7 and compares the result to 1.
Option D

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