Page 272 - Algebra 1

Example
2
Determining Rate of Change from a Table
A shop charges a fee for renting kayaks. What is the rate of change for the rental fees?
Time (hours)
2
4
6
8
Cost
$32.50
$60.50
$88.50
$116.50
SOLUTION Notice that the costs increase the same amount every 2 hours. Choose two sets of values from the table to find the ratio of the change in cost to the change in time.
Math Reasoning
Predict The rate of change is $14 per hour. How much would it cost to rent a kayak for 10 hours?
change in cost = 60.5 - 32.5 = 28 _____
change in time 4 - 2 2 The rate of change is $14 per hour.
Slope of a Line
4
2
O
y
The slope of a line is a rate of change.
It is equal to the ratio of the vertical
change (rise) to the horizontal change (run).
_ slope = rise run
run
(3, 5)
rise
x
(1, 1)
-4
-2
2
4
-4
y
Determining Slope from a Graph
Example
3
Find the slope of each line.
a.
SOLUTION Find the ratio of the rise to the run.
b.
y
4
4
2
(4,
1)
(1, 1)
rise x
x
O
-8
-4
4
-2
-2
2
(0
, -1)
run
-4 rise -8
8
-4
(4
, -8)
__ __
slope= rise = 2 run 4
= _1 2
slope= rise = -9 run 3
= - 3
SOLUTION Find the ratio of the rise to the run.
run
Lesson 41 257