Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 4.2 - 1

Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 4.2 - 2

Graphs, Linear Equations, and Functions

Chapter 4

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4.2

Slope of a Line

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4.2 Slope of a Line

Objectives

1. Find the slope of a line, given two points on the line.

2. Find the slope of a line, given an equation of the line.

3. Graph a line, given its slope and a point on the line.

4. Use slopes to determine whether two lines are parallel, perpendicular, or neither.

5. Solve problems involving average rate of change.

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4.2 Slope of a Line

Find the Slope of a Line Given Two Points on the Line

One of the important properties of a line is the rate at which it is increasing or decreasing. The slope is the ratio of vertical change, or rise, to horizontal change, or run.

12 ft

4 ft

P1

P2

As we move from P1 to P2:

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4.2 Slope of a Line

Find the Slope of a Line Given Two Points on the Line

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4.2 Slope of a Line

Finding the Slope of a Line

Find the slope of the line containing the points (–3, 1) and (3, 3).

Rise = 3 – 1 = 2

Run = 3 – (–3) = 6

There is a rise of 1 unit for a run of 3 units.

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4.2 Slope of a Line

Find the Slope of a Line given Two Points on the Line

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4.2 Slope of a Line

Find the Slope of a Line Given the Equation of the Line

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4.2 Slope of a Line

Finding the Slope of Horizontal and Vertical Lines

Find the slope of the line containing the points (–3, 2) and (4, 2).

Find the slope of the line containing the points (1, 3) and (1, –2).

Since the slope is 0, this is a horizontal line.

Since the slope is undefined, this is a vertical line.

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4.2 Slope of a Line

Finding the Slope from an Equation

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4.2 Slope of a Line

Using the Slope and a Point to Graph a Line

Locate the point P(–5, 5).

From the slope formula:

So, move down 2 units and then 3 units to the right to the point R(–2, 3).

Down 2

Right 3

P

R

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4.2 Slope of a Line

Orientation of a Line in the Plane

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4.2 Slope of a Line

Slopes of Parallel and Perpendicular Lines

Since parallel lines have the same slope, any line parallel to this line will have slope –2.

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4.2 Slope of a Line

Slopes of Parallel and Perpendicular Lines

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4.2 Slope of a Line

Slopes of Parallel and Perpendicular Lines

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4.2 Slope of a Line

Interpreting Slope as Average Rate of Change

Cindy purchased a new care in 2001 for $18,000. In 2006, the car had a value of $7500. At what rate is the car’s value changing with respect to time?