IXL | Write equations for proportional relationships from tables and graphs

Sean is determining the number of quarters equal to different dollar amounts.

There is a proportional relationship between the amount of money in dollars,

and the number of quarters,

Write an equation for the relationship between x and

Simplify any fractions.

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Learn with an example

question

Dominic has outgrown the bike he rode when he was small. So, for his twelfth birthday, his parents surprise him with a five-speed Blaze Rider 2000! Dominic has never had a bike with multiple speeds before, and he is eager to learn how it works. He starts by testing the middle speed.

There is a proportional relationship between the number of times Dominic pedals,

and the number of times the wheels rotate,

x (times Dominic pedals)	y (times the wheels rotate)
2	2
5	5
6	6
7	7

Write an equation for the relationship between x and

Simplify any fractions.

key idea

Two variables have a proportional relationship if the ratio of one variable to the other is constant.

A proportional relationship between x and y can be modeled by the equation

The letter k is the constant ratio of y to

It is called the constant of

proportionality.

solution

To write an equation for the relationship between x and

first find the constant of proportionality. Calculate the ratio of y to

x (times Dominic pedals)	y (times the wheels rotate)	Ratio of y to x (wheel rotations per time Dominic pedals)
2	2	2 2 = 1
5	5	5 5 = 1
6	6	6 6 = 1
7	7	7 7 = 1

The ratio for each pair of

and

y-values

So, the variables have a proportional relationship.

So, the constant of proportionality is 1 wheel rotation per time Dominic pedals.

Since the product

is commonly written without the 1, an equation for the relationship is:

Looking for more? Try these:

Lesson: Proportional relationships

$Confetti$

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Teacher tools

Work it out

Not feeling ready yet? These can help:

X.1Find the constant of proportionality from a table

X.4Find the constant of proportionality from a graph

Lesson: Proportional relationships

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