IXL | Write equations for proportional relationships from tables

While relaxing on his front porch, Marvin notices a garden snail crawling on the sidewalk. Marvin is amazed at how slowly the snail moves, so he starts timing it.

There is a proportional relationship between the amount of time (in minutes) that Marvin spends timing the snail,

and the distance (in feet) that the snail moves,

x (minutes)	y (feet)
1	2
3	6
5	10
9	18

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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