Compare Proportional Relationships

Compare Proportional Relationships

Compare Proportional Relationships​

Brooklyn, Taylor and Lincoln are three friends that competed in a race over the weekend.

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Can you tell, by looking at the different representations which runner was the fastest?​

In order to compare proportional relationships, we need to compare their unit rates.

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Since all proportional relationships pass the the origin, the only difference between them is their rates.​

​Compare Proportional Relationships

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Compare Proportional Relationships​

How could you determine Lincoln's speed from the table?

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Take a minute to examine the table before answering the next question​

Fill in the Blanks

Choose an ordered pair in the table and determine Lincoln's speed in miles per hour.

Lincoln runs

miles per hour.

Compare Proportional Relationships​

Taylor’s pace (shown on the graph) can be calculated similarly to Lincoln's.

Take a minute to examine the graph before answering the next question.​

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Fill in the Blanks

Taylor’s pace (shown on the graph) which can be calculated by dividing the y-coordinate by the x-coordinate.

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Find a point on the graph and use it to calculate the pace, in miles per hour, at which Taylor ran.

Taylor runs

miles per hour.

Compare Proportional Relationships​

In some cases, you may already be given information without having to do much work.​

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Brooklyn's speed is already given as a unit rate.

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Multiple Choice

Given all of this information, who ran the fastest between Lincoln, Taylor and Brooklyn?

• Lincoln

• Taylor

• Brooklyn

​Comparing Proportional Relationships

In order to compare proportional relationships​ we must compare their unit rates.

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To calculate the unit we can:

1)​ Create a ratio of y to x and divide.

2) Create a ratio of the rise to the run between two points and divide.​

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​Use an ordered pair and divide y by x.

​A sailboat and a speedboat each are traveling at a constant rate. The sailboat’s speed is summarized in the graph.

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The speedboat’s distance in terms of time is represented by the equation y = 60x, where x is the time in hours and y is the distance traveled in miles.

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Compare the speeds of the two boats.

​y=60x

​Speedboat

Fill in the Blanks

The unit rate of the sailboat is

miles per hour.

Click on the graph to zoom in, if needed.

Fill in the Blanks

Given the equation for the speedboat.....

y=60x

The speedboat travels

miles per hour.

Open Ended

Which boat traveled faster?

How do you know?

Multiple Choice

If you were to graph the speedboat's speed on the same graph as the sailboat's, which line would be steeper?

• The sailboat's line would be steeper than the motorboat's.

• The speedboat's line would be steeper than sailboat's.

​The height of a hot air balloon over time is given in the following table.

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The height of a blimp over time is given by y = 250x, where y represents the height in feet and x represents the time in minutes.

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Fill in the Blanks

How fast is the hot air balloon rising?

The hot air balloon is rising

feet per minute.

Fill in the Blanks

Given the equation y=250x, how fast is the blimp rising?

The blimp is rising

feet per minute.

Multiple Choice

Is the blimp or hot air balloon rising faster?

• Hot air balloon

• Blimp

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​​A grocery store and a street vendor are each selling bananas by the pound. Below you can see some information about the cost of bananas at both places.

​Banana Costs

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​You can buy 2 pounds of bananas from a street vendor for $1.62. The cost of bananas at a grocery store is shown in the photo.

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​Street Vendor

​Grocery Store

Fill in the Blanks

If the street vendor charges $1.62 for 2 pounds of bananas, this means is would cost $

per pound for bananas.

Multiple Choice

Is it a better deal to get bananas at the street vendor or the grocery store?

• Street Vendor

• Grocery Store