IXL | Identify proportional relationships: word problems

A receptionist named Eli spends 4 minutes routing each incoming phone call. Is the total number of minutes on the phone proportional to the number of phone calls routed?

yes

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Learn with an example

question

Carter cycles 4 kilometers during each trip to work. Is the total distance cycled proportional to the number of trips to work?

yes

key idea

Proportional quantities can be described by the equation y = kx, where k is a constant ratio.

solution

You can check that the relationship is directly proportional by showing that the relationship can be written as y = kx, where k is a constant ratio.

First, create a chart.

Total distance cycled (kilometers) (y)	4	8	12	16
Number of trips to work (x)	1	2	3	4

Now divide "Total distance cycled (kilometers) (y)" by "Number of trips to work (x)" to find the ratio (k).

Total distance cycled (kilometers) (y)	4	8	12	16
Number of trips to work (x)	1	2	3	4
Ratio (k)	4	4	4	4

The ratio is constant (k = 4), so the relationship can be described by the equation y = 4x. This equation means that the total distance cycled (kilometers) is always 4 times the number of trips to work.

Because the relationship can be written as y = 4x, the relationship is directly proportional.

Looking for more? Try these:

Lesson: Proportional relationships

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Not feeling ready yet? These can help:

X.7Identify proportional relationships from tables

X.6Identify proportional relationships from graphs and equations

Lesson: Proportional relationships

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