4.4 Finding Slope and Rate of

Change

How Would You Describe Slope?

Slope

A ratio of the vertical change (rise) to the horizontal change (run)Rise/run

Change in y/Change in x

y2 – y1/x2 – x1

Examples: Find the Slope

1. (4, 3) (2, -1)

2. (-1, -1) (6, -2)

3. (8, 2) (3, 4)

Can do these visually, see example 1 page 235, but do not rely on this as numbers start getting bigger!

Guided Practice 1-3 on Page 235

Horizontal and Vertical Lines

(2, 1) (2, 9)

(-7, 8) (-7, 10)

(5, 4) (10, 4)

(7, -2) (2, -2)

Guided Practice 4-6 page 236

What do the lines of these slopes look like?

Positive Slope

Negative Slope

Zero Slope

Undefined Slope

Rate of Change

Compares a change in one quantity to a change in another quantity.

Why is slope also a rate of change?

Do guided practice #7

Extra Example (not in book- add to notes)

The table shows the cost to paint a house for a given number of hours. Find the rate of change in cost with respect to time.

Time (hours) 4 6 8

Cost ($) 90 135 180

Rates of Change and Line Graphs

Break line graph into segmentsFind slope of each segmentUse the slopes to describe the change

EXAMPLE 6 Use a graph to find and compare rates of change

COMMUNITY THEATER

A community theater performed a play each Saturday evening for 10 consecutive weeks. The graph shows the attendance for the performances in weeks 1, 4, 6, and 10. Describe the rates of change in attendance with respect to time.

Extra Example 7

The graph shows the number of computer games sold day 1, day 4, day 7 and day 9 of a sale. Describe the rates of change in sales with respect to time.

Interpreting a Graph

Look over what is on each axis and what is being described. Decide what the different points on the graph are representing.

Example 7 and Guided Practice # 9

Find a Coordinate Given a Slope

(0, y), (-2,1); m = -8

(-3, y + 1), (0, 4); m = 6

Review

How do you find slope?What is rate of change and how do you

find it?What are important things to look for when

you’re interpreting a graph? How can you find a coordinate given a

point and a slope?

Homework

1 – 6, 8 – 32 even, 33, 34, 36 – 40

Bonus Problems: 35, 41