IXL | Write equations for proportional relationships from tables: with decimals

The Picture and Sound electronics store has hired Tim to work in the warehouse. He uses a pulley with a hand crank to lift heavy boxes.

There is a proportional relationship between the number of times Tim turns the crank to lift a box,

and the height the box has been lifted (in feet),

x (times Tim turns the crank)	y (feet)
5	2.2
10	4.4
15	6.6
20	8.8

Write an equation for the relationship between x and

Simplify any fractions.

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question

The Picture and Sound electronics store has hired Bridgette to work in the warehouse. She uses a pulley with a hand crank to lift heavy boxes.

There is a proportional relationship between the number of times Bridgette turns the crank to lift a box,

and the height the box has been lifted (in feet),

x (times Bridgette turns the crank)	y (feet)
5	1.3
10	2.6
15	3.9
20	5.2

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 Bridgette turns the crank)	y (feet)	Ratio of y to x (feet per time Bridgette turns the crank)
5	1.3	1.3 5 = 0.26
10	2.6	2.6 10 = 0.26
15	3.9	3.9 15 = 0.26
20	5.2	5.2 20 = 0.26

The ratio for each pair of

and

y-values

0.26.

So, the variables have a proportional relationship.

So, the constant of proportionality is 0.26 feet per time Bridgette turns the crank.

The equation for the relationship is:

0.26

Looking for more? Try these:

Lesson: Proportional relationships

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Lesson: Proportional relationships

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