UNIT 5.04

Comparing Rates

I can compare Unit Rates from word problems, tables, linear equations and

graphs!

Vocabulary

Finding the Unit Rate from the graph of a line: The graph of a line consists of an infinite number of points, any of which can be used to find the Unit Rate (or Constant Rate of Change) of the line.

Step 1: Pick two points (chose points whose coordinates are whole numbers, i.e. hit the grid perfectly)

Step 2: Draw a right triangle where these two points form its hypotenuse.

Step 3: Count and label the length of each leg. Step 4: Calculate the “change in y” divided by the “change in

x” and simplify it as much as possible (still in fraction form). This is the Unit Rate, or Constant Rate of Change, for these points.

Vocabulary

Example: Step 1: Pick two points Step 2: Draw a right triangleStep 3: Find length of legsStep 4: Find the Unit Rate

A

B

10

6

✓✓

✓✓

Now You Try It!1)

A

B

8

6

Step 1: Pick two points Step 2: Draw a right triangleStep 3: Find length of legsStep 4: Find the Unit Rate

✓✓

✓✓

Let’s Try It!2)

9

123

4

6

8

Step 1: Pick two points Step 2: Draw a right triangleStep 3: Find length of legsStep 4: Find the Unit Rate

✓✓

✓✓

Let’s Compare!

Example: Skye, Hunter and Brooke all competed in a swimming race. Their speeds are represented below. Find and compare all three Speeds (Unit Rates). Then, list the swimmers in order, fastest to slowest.

Seconds (x)

Meters (y)

0 0

4 6

8 12

12 18

Unit Rates:

Skye:

____________

Hunter:

____________

Brooke:

____________

Skye, Brooke, Hunter!

1st place 2nd place 3rd place

1.5 m. per sec.

0.75 m. per sec.

1.25 m. per sec.

Let’s Try It!

Dennis, Maggie & Luis each rented a car. Find and compare all three car rental rates (Unit Rates). Who got the best deal? List them in order, best to worst!

Days (x)

Cost (y)

2$156.0

0

3$234.0

0

4$312.0

0

Unit Rates:

Dennis:

____________

Maggie:

____________

Luis:

____________

Luis, Dennis, Maggie!Best deal! 2nd best Worst deal!

$78 per day

3)

$79 per day

$75 per day

Let’s Try It!

Jeff, Jared and Eric love to send text messages to their friends! Find and compare all three rates of texts sent (Unit Rates). Who sent the most texts per day? List them in order, least to greatest!

Days (x)

Texts (y)

3 450

6 900

9 1350

Unit Rates:

Jeff:

____________

Jared:

____________

Eric:

____________

Eric, Jeff, Jared!Least, Middle, Most!

150 per day

4)

160 per day

100 per day

Sent 4800

texts in 30 days!

5.04 COMPARING RATES WS

Homework Time!

I can compare Unit Rates from word problems, tables, linear equations and

graphs!