# COMPARE AND INTERPRET THE CONSTANT OF PROPORTIONALITY WORKSHEET

Give the slope of the graph and the unit rate.

Problem 1 :

Jorge: 5 miles every 6 hours

Problem 2 :

A supply company sell packs of paper by the box. Each box contains the same number of packs of paper, P. Which equation can be used to find the total number of of packs of paper, T, that would be in B boxes ordered ?

a) B + P = T     b)  P/B = T     c)  BP = T     d) B/P = T

Solution

Problem 3 :

Which equation could be used to find the number of days d in h hours ?

a) 24/h = d     b)  24 + h = d     c)  24h = d     d) h/24 = d

Solution

Problem 4 :

The graph below shoes how much plant grew monthly.

Based on the graph, what does the point (2, 60) represent ?

a) The plant grew 2 cm in 60 months.

b) The plant grew 60 cm in 2 months.

c)  The plant grew 30 cm in 2 months.

d) The plant grew 60 cm in 2 days.

Solution

Problem 5 :

Russell conducted an experiment where he collected snow in container, measured it, then measured the amount of water in the container after the snow had melted. He created the graph below to display his findings.

Based on the graph, what does the point (0, 0) represent ?

a) The collection of 0 inches of snow results in no water.

b) The collection of 0 inches of water results in no snow.

c) The amount of snow was not proportional to the amount of water.

Solution

Problem 6 :

Each table represents a proportional relationship. For each, find the constant of proportionality, and write an equation that represents the relationship.

Solution

Problem 7 :

A recipe says that 2 cups of dry rice will serve 6 people. Complete the table as you answer the questions.

a. How many people will 10 cups of rice serve?

b. How many cups of rice are needed to serve 45 people?

Solution

Problem 8 :

A recipe says that 2 cups of dry rice will serve 6 people. Complete the table as you answer the questions.

a. How many people will 1 cup of rice serve?

b. How many people will 3 cups of rice serve? 12 cups? 43 cups?

c. How many people will x cups of rice serve?

Solution

Problem 9 :

A factory produces widgets at a constant rate. After 4 hours, 3,120 widgets have been produced. At what rate are the widgets being produced?

a) 630 widgets per hour       b) 708 widgets per hour

c) 780 widgets per hour       d) 1,365 widgets per hour

Solution

Problem 10 :

There are 3 cans that store 9 tennis balls. Consider the number of balls per can.

a) Find the constant of proportionality for this situation.

b) What does it mean for this situation?

c) Write an equation to represent the relationship.

Solution

1)  k = 5/6

2)  T = BP

3)  d = h/24

4)  It grew 60 cm in 2 months.

5)  The collection of 0 inches of snow results in no water.

6)  P = 4s

7)  a. So, 10 cups of rice can be served for 30 people.

b. So, 15 cups of rice is needed.

8)  k = 3, x = 3 then y = 9

x = 12 then y = 36

x = 43 then y = 129

9)  1 hour = 720 widgets

10)  a) Constant of proportionality = 3

b) Each can will store 3 balls.

c) Equation y = 3x

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