Practice Proportional Function in Math

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

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Quick Recap

A proportional function has the form $f(x) = kx$ for a constant $k \neq 0$ — it passes through the origin and the ratio $f(x)/x = k$ is constant.

Double the input, double the output. No offset—starts at zero.

Showing a random 20 of 50 problems.

Example 1

challenge

Two quantities satisfy

y=kx

. Doubling

x

and the formula's

k

both. What is the net effect on

y

Example 2

medium

For a proportional function, what is the ratio

y/x

at every point?

Example 3

medium

For

y = \tfrac{3}{4}x

, find the value of

x

for which

y = 9

Example 4

medium

Determine whether

(2, 5), (4, 11), (6, 17)

lie on a proportional function.

Example 5

easy

Does the graph of

y = 4x - 3

pass through the origin?

Example 6

easy

For

y = \tfrac{1}{2}x

, find

y

when

x = 10

Example 7

challenge

Let

f(x) = kx

be proportional. Show that

f(a) + f(b) = f(a + b)

for all real

a, b

, and explain why this fails for

f(x) = kx + c

with

c \neq 0

Example 8

hard

f

is proportional and

f(2) + f(5) = 49

, find

f(10)

Example 9

medium

A graph of

y = kx

passes through

(-3, 12)

. Find

k

and write the equation.

Example 10

easy

Must a proportional function pass through

(0,0)

Example 11

medium

A recipe uses

3

cups of flour for

12

cookies. Write the proportional function and find flour for

20

cookies.

Example 12

easy

The weight of water is proportional to its volume.

5

liters weighs

5

kg. Write the function, find the constant of proportionality

k

, and compute the weight of

8.5

liters.

Example 13

easy

For the proportional function

y = 6x

, find

y

when

x = 4

Example 14

medium

Which graph is proportional: line through

(0,0)

and

(2,4)

, or through

(0,3)

and

(2,7)

Example 15

easy

Hooke's Law states spring force is proportional to stretch:

F = kx

. If

F = 30

N when

x = 6

cm, find

k

and the force when

x = 10

cm.

Example 16

medium

Which of the following are proportional: (a)

y = 7x

, (b)

y = x + 3

, (c)

y = -x

, (d)

y = x^2

Example 17

medium

Write the proportional function whose graph passes through

(5, -20)

and find

y

when

x = -2

Example 18

medium

(1,2),(2,5),(3,8)

proportional?

Example 19

medium

Determine whether

y

is proportional to

x

given the table:

x: 2, 4, 6

and

y: 7, 14, 21

. If yes, find

k

and the equation.

Example 20

challenge

Suppose

y

is proportional to

x

and

z

is proportional to

y

, with constants

k_1

and

k_2

. Express

z

as a proportional function of

x

, and state the new constant.

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Related Concepts

Linear Functions Proportional Relationships Direct Variation Constant of Proportionality