Interpreting the unit rate as slope

Interpreting the unit rate as slope

Recall Unit Rate

A unit rate is a rate in which the second quantity in the comparison is one unit. 
Examples: miles per hour; price per pound

Multiple Select

Which of the following are unit rates? (More than one may be correct.)

• 60mph

• $5.75 per 2 pounds

• 5 oranges per 1 apple

• 25 rpm

• $37 per 4 sweaters

Slope vs. Unit Rate

Slope = rise over run = change in y over change in x
Unit rate = change in one quantity over change in second quantity
Slope = unit rate

Consider the following.

A storm is raging on Misty Mountain. The graph shows the constant rate of change of the snow level on the mountain. 

Open Ended

What do you notice about the amount of snow on the mountain with respect to the time?

Multiple Choice

Find the slope between the points (1,2) and (5, 10). Remember that slope is the constant rate of change.

• 1/2

• 2

• -1/2

• -2

Multiple Choice

What is the unit rate of snowfall in inches per hour?

• 1/2

• 2

• -1/2

• -2

Multiple Select

Which unique point on the graph gives you the slope of the graph AND the unit rate of change in the snow level?

• (0, 0)

• (1, 2)

• (2, 4)

• (5, 10)

Open Ended

Why does the point (1, 2) show the slope AND the unit rate of change in snow level?

Slope and Constant of Proportionality

When you graph a proportional relationship, the constant of proportionality is the same as the slope. 

Every 3 pounds of bananas cost $1.

This is a graph of the price of bananas per pound using the statement above. 

Multiple Choice

What is the unit rate of the price of bananas?

• $3 per pound

• $0.33 per pound

Multiple Choice

What is the slope of this graph?

• 3/1

• 1/3

• -3/1

• -1/3

Open Ended

Extrapolate. Name another point that will be on the graph, but that you cannot see.