IXL | Compare proportional relationships represented in different ways

Each day after school, Haley rides either her road bike or her cruiser bike through the park. There is a proportional relationship between the amount of time she spends riding and the distance she travels.

The equation below describes how far Haley travels on her road bike. In the equation,

represents the distance in meters that she travels in

minutes:

175

This graph shows how far Haley travels on her cruiser bike:

Which bike does Haley ride faster?

road bike

cruiser bike

How far can she travel on that bike in 5 minutes?

meters

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Learn with an example

question

Haley and Owen work part-time jobs on the weekends. Haley works at a frozen yogurt stand, and Owen works at a hot dog stand. There is a proportional relationship between the number of hours they each work and the amount of money they each earn. This table shows how much money Haley earns:

Haley's earnings
Hours worked	Earnings
4	$45
8	$90
12	$135

This graph shows how much money Owen earns:

Who earns more money per hour?

Haley

Owen

How much would that person earn for 7 hours of work?

key idea

Two quantities have a proportional relationship if they have a constant unit rate. To find the unit rate, divide one quantity by the other quantity.

solution

Find the unit rate for each person. Then, compare the two rates.

Start with Haley. You can use any row in the table to find her unit rate. For example, the first row tells you that Haley earns $45 for 4 hours of work. Find the unit rate.

hours

11.25

hour

So, Haley earns $11.25 per

hour.

Next, find the unit rate for Owen. You can use any point on the line to find his unit rate. For example, the point

(

)

tells you that Owen earns $60 for 5 hours of work.

Find the unit rate.

hours

hour

So, Owen earns $12 per

hour.

Now, compare the two unit rates. Since $12 per hour is more than $11.25 per hour, Owen earns more money per hour than Haley does.

Last, find how much Owen would earn for 7 hours of work. Multiply by his unit rate.

per hour

hours

So, Owen would earn $84 for 7 hours of work.

Looking for more? Try this:

$Confetti$

Excellent!

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Time
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Teacher tools

Work it out

Not feeling ready yet? These can help:

X.1Find the constant of proportionality from a table

X.4Find the constant of proportionality from a graph

L.9Compare rates: word problems

X.11Write and solve equations for proportional relationships

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