Page 271 - Algebra 1

L E S S O N Finding Rates of Change and Slope 41
Warm Up
1. Vocabulary A (literal, linear) equation is an equation whose
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graph is a straight line.
2. Find the range of the function f(x) = 2x + 3 for the domain {0, 1, 2}.
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Name the quadrant on the coordinate plane in which the following points are located:
3. (3, -5) 4. (-3, -5) 5. (-5, 3) (20) (20) (20)
New Concepts A rate of change is a ratio that compares the change in one quantity with the change in another. For example, the speed of a car is a rate of change that
compares the distance and the time traveled.
Exploration Analyzing a Graph
Arvand leaves his house and jogs to Cory’s house. Later they walk to a local pizza 2
shop. The graph shows the distance Arvand traveled between the time he left home and
when he arrived at the pizza shop. 0
a. When was Arvand traveling the fastest?
1
4 8 12 16 20
Time (min)
b. How long was Arvand at Cory’s house? How can you tell?
c. Compare the graph during the times Arvand was jogging to Cory’s
and when they were walking to the pizza shop.
Determining Rate of Change from a Graph
Example
1
A car travels on a highway at a constant speed. The graph shows the relationship between the distance traveled and the time traveled. Find the rate of change.
100 60 20
(2, 120)
(1, 60)
SOLUTION Choose two points on the graph and find the ratio of the change in distance to the change in time.
1 2
Time (hours)
Hint
You can use any two points on the line to determine the rate of change.
change in distance = 120 - 60 ___
2 - 1
The rate of change is 60 miles per hour.
change in time
= 60
Online Connection www.SaxonMathResources.com
256 Saxon Algebra 1
Distance (mi)
Distance (mi)