IXL | Write and solve equations for proportional relationships

Read the description of a proportional relationship.

Julia has outgrown the bike she rode when she was small. So, for her twelfth birthday, her parents surprise her with a five-speed Blaze Rider 2000! Julia has never had a bike with multiple speeds before, and she is eager to learn how it works. She starts by testing the middle speed. There is a proportional relationship between the number of

times Julia pedals

, and the number of

times the wheels rotate

When she pedals 1

time,

the wheels rotate 3

times.

Write the equation for the relationship between x and

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Learn with an example

question

Read the description of a proportional relationship.

As a farmer, Richard keeps a close eye on the weather. After a few stressful weeks with no rain, Richard was relieved when it started raining one morning. It rained steadily all day, and Richard periodically checked to see how much rain had fallen. There is a proportional relationship between the amount of time (in

hours

) it had been raining,

, and the amount of rain (in

inches

) that had fallen,

After 4

hours,

a total of 1 inch of rain had fallen. Write the equation for the relationship between x and

key idea

A proportional relationship between x and y can be modeled by y =

kx.

In this equation, k is the constant ratio of y to

It is called the constant of

proportionality.

solution

There is a proportional relationship between the amount of time (in

hours)

it had been raining,

and the amount of rain (in

inches)

that had fallen,

To write the equation for this relationship, find

Use the numbers given in the problem and their units.

After 4

hours,

a total of 1 inch of rain had fallen.

When the

x-value

is 4, the

y-value

is 1. Now calculate

the ratio of y to

0.25

Plug k = 0.25 into the equation y = kx to find the equation for this relationship.

0.25

Looking for more? Try these:

Lesson: Proportional relationships

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Work it out

Not feeling ready yet? These can help:

X.2Write equations for proportional relationships from tables

AA.10Solve one-step equations with whole numbers

Lesson: Proportional relationships

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