IXL | Find the constant of proportionality from a table

A mysterious flying superhero known as Blue Sky protects the good citizens of Oxford. Unknown to these citizens, Blue Sky is actually mild-mannered Trudy, a scientist in a flying suit. Before Trudy can fly in the suit, she needs to charge its battery.

There is a proportional relationship between the number of hours Trudy has charged her flying suit,

and the number of hours she can fly,

x (hours charged)	y (flight hours)
1	1
4	4
7	7
8	8

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

flight hours per hour charged

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Learn with an example

question

Carter is hooked on a new book series, The

Galaxy.

Each book in the series is the same length and chronicles a different year in the Waka Waka Galaxy. Carter has cleared off the top shelf of his bookcase to leave room for each of the books as they come out.

There is a proportional relationship between the number of books on the shelf,

and how much shelf space the books take up (in inches),

x (books)	y (inches)
2	2
11	11
13	13
16	16

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

inches per book

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 (books)	y (inches)	Ratio of y to x (inches per book)
2	2	2 2 = 1
11	11	11 11 = 1
13	13	13 13 = 1
16	16	16 16 = 1

The ratio for each pair of

and

y-values

So, the variables have a proportional relationship.

So, the constant of proportionality is 1 inch per book.

Looking for more? Try these:

Lesson: Proportional relationships

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Lesson: Proportional relationships

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