IXL | Find the constant of proportionality from a table: with decimals

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

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

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

x (pounds)	y (dollars)
9	$4.50
12	$6
16	$8
19	$9.50

What is the constant of proportionality? Write your answer as a whole number or decimal.

dollars per pound

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Learn with an example

question

Clare is throwing a pool party to kick off the summer. Her pool is empty, so she starts filling it with water from a garden hose.

There is a proportional relationship between the time Clare has been filling up the pool (in minutes),

and the volume of water in the pool (in gallons),

x (minutes)	y (gallons)
0.5	5
0.8	8
1.5	15
1.6	16

What is the constant of proportionality? Write your answer as a whole number or decimal.

gallons per minute

key idea

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

If x and y have a proportional relationship, the constant of proportionality is the ratio of y to

solution

To find the constant of proportionality, calculate the ratio of y to

x (minutes)	y (gallons)	Ratio of y to x (gallons per minute)
0.5	5	5 0.5 = 10
0.8	8	8 0.8 = 10
1.5	15	15 1.5 = 10
1.6	16	16 1.6 = 10

The ratio for each pair of

and

y-values

10.

So, the variables have a proportional relationship.

So, the constant of proportionality is 10 gallons per minute.

Looking for more? Try these:

Lesson: Proportional relationships

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Lesson: Proportional relationships

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