CS 2.3: Finding Costs – Unit Rate and Constant of Proportionality
KEY
The unit rate of one pizza at Howdy’s is $13. The equation P = 13n relates the price of the pizza and the number of pizzas. This
equation represents a proportional relationship
because you multiply one variable by a constant number to get the value of the other variable. The constant multiplier is
called the constant of proportionality
If a delivery charge of $5 is added to the cost, the relationship is no longer proportional.
P = 13n + 5 is not a proportional relationship.
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A. Graph the two equations for the oranges problem on separate coordinate grids.
a. Think about how to scale your graph on each axis before you start plotting points.
b. Look at the tables that you created on page 9 so that you can find coordinates to plot.
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B. Noralie’s car uses 20 gallons of gas to go 600 miles.
Rate Table
0
0
1
30
Graph
2
60
4
120
10
300
10.5
315
Find the unit rate
(miles per gallon) by
using the graph:
Find the missing values in the table.
Find the unit rate (miles per gallon) by using the table:
Unit Rate:
30 miles per gallon
How can you tell by looking the table that this is a
proportional relationship?
What does (1,30)
mean?
The table increase by 30 miles for every gallon.
1 gallon = 30 miles
Equation
Find the equation for this situation:
d = 30g
(d=distance, g=gallons)
How can you tell by looking the equation that this is a
proportional relationship?
For every gallon used,
the distance will increase by 30 miles
Use the graph to find how many miles she can drive with 4
gallons of gas.
(4, 120)
= 120 miles
How can you tell by looking the graph that this is a
proportional relationship?
The rate moves in a straight line.
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