IXL | Write equations for proportional relationships from tables

Bryan's space shuttle crew accidentally left him behind on a mysterious planet. He soon realizes that his body is aging much faster on this planet than it did on Earth.

There is a proportional relationship between the number of weeks Bryan spends on the planet,

and the number of years he ages,

x (weeks)	y (years)
1	3
2	6
3	9
4	12

Write an equation for the relationship between x and

Simplify any fractions.

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Learn with an example

question

To help the environment and make some extra money, Dale takes his empty cans to the Cash Not Trash recycling shop. The shop pays cash based on the total weight of the cans Dale brings in for recycling.

There is a proportional relationship between the weight (in pounds) of the cans Dale brings into the shop,

and the amount (in dollars) the shop pays Dale,

x (pounds)	y (dollars)
6	$3
8	$4
14	$7
16	$8

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 (pounds)	y (dollars)	Ratio of y to x (dollars per pound)
6	$3	3 6 = 0.50
8	$4	4 8 = 0.50
14	$7	7 14 = 0.50
16	$8	8 16 = 0.50

The ratio for each pair of

and

y-values

0.50.

So, the variables have a proportional relationship.

So, the constant of proportionality is 0.50 dollars per pound.

The equation for the relationship is:

0.5

Looking for more? Try these:

Lesson: Proportional relationships

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N.1Find the constant of proportionality from a table

Lesson: Proportional relationships

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