Finding Rate in a Table

Finding Rate in Tables

What is a rate?

• Remember: rates must have TWO units, such as miles PER hour or meters PER second

• Therefore, we have to look at BOTH SIDES of the table

• For linear relationships, we always want to find the UNIT RATE (per 1)

Multiple Choice

What is Peach's rate of change?

Make sure it's the unit rate!

• 1 meter per second

• 3 meters per 3 seconds

• 45 meters per second

Multiple Choice

What is the rate in this table?

• 1

• 3

• 4

• 16

Rate = 3

• When the x goes up by 1,

  the y goes up by 3

• When x changes by 2 (from 2 to 4), the y changes by 6. The UNIT RATE is still 3 because 6/2 = 3.

Multiple Choice

A tree's height was recorded over several years.

What is the rate? (UNIT rate)

• 3 inches per year

• 5 inches per year

• 0 years per inch

• 15 inches per year

Rate = 3 inches per year

• The table changed by 15, but that was per 5 years

• If we find the UNIT RATE, it is 3 inches per year

• Notice the order of the rate. We say inches per year because "years per inch" doesn't make sense!

Multiple Choice

Find the rate.

• 3

• -3

• 20

• -6

Multiple Choice

What is the rate? (unit rate)

• $1 per hour

• $40 per hour

• $5 per hour

• $10 per hour

Rate = $5 per hour

Multiple Choice

Find the rate of change.

• -2 minutes per gallon

• -20 minutes per gallon

• -2 gallons per minute

• -20 gallons per minute

Rate = -2 gallons per minute

• Pay close attention to whether the rate is increasing (positive) or decreasing (negative)

Multiple Choice

Did you notice the order we put the rate in each time?

Which of these matches the order of the fraction at the bottom of the picture?

Rate Formula

• Mathematicians like to have a standardized way to do things

• EVERY TIME you find rate, this is the order we write the fraction in

Multiple Choice

Let's try it together! We are trying to find

change in y / change in x

Look at the first two rows of the table.

What is the change in JUST the y's?

• 2

• 4

• 13

• 17

Multiple Choice

Let's try it together! We are trying to find

change in y / change in x

Look at the first two rows of the table.

Change in y = 4

What is the change in the x's?

• 2

• 4

• 5

• 7

Rate = 4/2 = 2

• Change in y = 4. It goes on top of the fraction

• Change in x = 2. It goes on the bottom

• Now simplify!

• It ALWAYS goes in this order

Multiple Choice

What is the rate?

Use change in y / change in x.

• 1/3

• 3

• 7

• 2

Rate = 3/1 = 3

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Multiple Choice

What is the rate?

Use change in y / change in x.

• 3

• 11

• 4

• 8

Rate = 8/2 = 4

Multiple Choice

What is the rate?

Use change in y / change in x.

Hint: if you don't want to use the negatives, you can use ANY two points in the table.

• 5

• 3

• 9

• 7

Rate = 9/3 = 3

Multiple Choice

What is the rate?

Use change in y / change in x.

***Notice the table flipped sideways***

Make sure to still look at change between two points

• 11

• 4

• 5

• 10

Rate = 10/2 = 5

Now keep practicing!

Make sure to use change in y / change in x.

Multiple Choice

What is the rate?

Use change in y / change in x.

• 2 hours per day

• 1/6 hour per day

• 12 hours per day

• 6 hour per day

Multiple Choice

What is the rate?

Use change in y / change in x.

• $75 per hour

• $3 per hour

• $25 per hour

• $15 per hour

Multiple Choice

What is the rate?

Use change in y / change in x.

Hint: You can look at any of the 2 points.

Also, if an answer is a fraction, keep it that way - just make sure change in y goes on top!

• 3

• 2

• 2/3

• 3/2

Multiple Choice

What is the rate?

Use change in y / change in x.

• 40 CALORIES PER MIN.

• 15 CALORIES PER MIN.

• 4 CALORIES PER MIN.

• 60 CALORIES PER MIN.