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3-1 Rate of Change and Slope
The table shows the horizontal and vertical distances from the base of the
mountain at several poles along the path of a ski lift. The poles are connected
by cable. Between which two poles is the cable’s path the steepest? How do
you know?
Create Representations to Communicate Mathematical Ideas (1)(E) Describe
how the representation you made successfully organizes and communicates your
solution to the problem.
A
B
C
D
20
40
60
100
30
35
60
70
Horizontal
Distance
Vertical
DistancePole Online
Vocabulary
ExplorationInteractive
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Lesson 3-1 | Rate of Change and Slope
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Problem 1 Got It?Pr
Problem 2 Got It?Pr Finding the Rate of Change of a Linear Function
What is the rate of change of the linear function that passes through the points
(-4, 3) and (5, -9)?
Finding Rate of Change and Slope Using a Table
The table shows the cost of a certain amount of nuts. What does the rate of
change represent in this context? Determine whether the data represent a linear
relationship. If so, find the slope of the line containing the points given in the table.
Weight(oz)
Cost($)
1.25
2.50
3.75
5.00
16
32
48
64
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Lesson 3-1 | Rate of Change and Slope
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Problem 3 Got It?Pr Finding Slope Using a Graph
What is the slope of each line?
a.
b.
c. In part (a), pick two new points on the line and find the slope. Do you get the
same slope?
Discuss the terms rate of change and slope with a classmate. Listen to your
classmate explain the steps used to solve part (a). Repeat back the steps to
explain how to solve part (b). Together complete the problem.
TEKS Process Standard (1)(D)
x
y
O2224 2 4
3
1
x
y
O22
22
24 2
2
ELPELPELPELPELPELPELPELPELPELPELPELPELPELPELPSSSSSSELPELPELPS
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Lesson 3-1 | Rate of Change and Slope
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Problem 4 Got It?Pr Finding Slope Using Points
a. What is the slope of the line through (1, 3) and (4, -1)?
b. Plot the points in part (a) and draw a line through them. Does the slope of the
line look as you expected it to? Explain.
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Problem 5 Got It?Pr
Problem 6 Got It?Pr Finding Slopes of Horizontal and Vertical Lines
What is the slope of the line through the given points?
a. (4, -3), (4, 2)
b. (-1, -3), (5, -3)
TEKS Process Standard (1)(G)
Finding Rate of Change in Real-World Situations
A train traveling at a constant rate is 120 km from its destination at 1:00 pm. The
train is 88 km from its destination at 1:24 pm. Determine the rate of change.Learning
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Lesson 3-1 | Rate of Change and Slope
