Practice Constant of Proportionality in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

The constant ratio $k$ between two proportional quantities: if $y = kx$ , then $k$ is the constant of proportionality.

If $y$ is always 3 times $x$ , the constant of proportionality is 3.

Showing a random 20 of 50 problems.

Example 1

medium

y = kx

and

y = 18

when

x = 6

, find

y

when

x = 10

Example 2

medium

A recipe uses

k

cups of flour per cookie.

24

cookies use

6

cups. Find

k

and the flour for

40

cookies.

Example 3

hard

Three quantities:

y \propto x

with

k_1

, and

z \propto y

with

k_2

. If

k_1 = 3

and

k_2 = 4

, what is the constant relating

z

and

x

Example 4

easy

Find

k

for

y = kx

given

x = 7, y = 21

Example 5

medium

A table:

(x,y) = (2,9),(4,18),(6,27)

. Is it proportional? Find

k

Example 6

easy

If two quantities are proportional with

k=1

, what is true about

x

and

y

Example 7

medium

A spring stretches proportionally:

2

N stretches it

5

cm. Find

k

(cm per N) and the stretch for

7

Example 8

medium

A table has

(x,y)

(1,3),(2,6),(3,10)

. Find

k

from the first row and test if proportional.

Example 9

medium

y

is proportional to

x

y=21

when

x=3

. Find

y

when

x=8

Example 10

challenge

y = kx + b

describes a line. For what

b

is the relation a proportional relationship?

Example 11

hard

Two quantities are proportional. Increasing

x

6

increases

y

15

. Find

k

Example 12

easy

y = 5x

, what is the constant of proportionality?

Example 13

easy

A bag of

5

oranges costs $3. Find

k

in cost

= k \cdot

(number of oranges).

Example 14

medium

k

pages/minute, a printer made

84

pages in

4

minutes. Find

k

Example 15

medium

Graph of

y=kx

passes through

(5, 12)

. Find

y

when

x = 15

Example 16

easy

y = 8x

, what is the constant of proportionality?

Example 17

medium

y = kx

has

k = 0.25

. Find

y

when

x=20

and

x

when

y=11

Example 18

medium

A printer prints proportionally:

90

pages in

3

minutes. Find

k

(pages/min) and pages in

7

minutes.

Example 19

medium

A recipe scales proportionally:

3

cups flour make

24

cookies. How many cookies from

5

cups?

Example 20

easy

For

y=kx

, what does the graph look like?

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Related Concepts

Proportional Relationships Ratios Linear Functions Slope