- Submitted By: Siti-Hamdani
- Date Submitted: 05/25/2015 6:14 PM
- Category: Science
- Words: 1929
- Page: 8

INTRODUCTORY MATHEMATICAL

ANALYSIS

For Business, Economics,

and the Life and Social Sciences

Chapter 3

Lines, Parabolas, and Systems

2011 Pearson Education, Inc.

Chapter 3: Lines, Parabolas and Systems

Chapter Outline

3.1) Lines

3.2) Applications and Linear Functions

3.3) Quadratic Functions

3.4) Systems of Linear Equations

3.5) Nonlinear Systems

3.6) Applications of Systems of Equations

2011 Pearson Education, Inc.

Chapter 3: Lines, Parabolas and Systems

3.1 Lines

Slope of a Line

• The slope of the line is for two different points

(x1, y1) and (x2, y2) is

y 2 y1

vertical change

m

x 2 x1 horizontal change

2011 Pearson Education, Inc.

Chapter 3: Lines, Parabolas and Systems

3.1 Lines

Example 1 – Price-Quantity Relationship

The line in the figure shows the relationship

between the price p of a widget (in dollars) and the

quantity q of widgets (in thousands) that consumers

will buy at that price. Find and interpret the slope.

2011 Pearson Education, Inc.

Chapter 3: Lines, Parabolas and Systems

3.1 Lines

Example 1 – Price-Quantity Relationship

Solution:

The slope is

p2 p1 1 4

1

m

q2 q1 8 2

2

Equations of lines

• A point-slope form of an equation of the line

through (x1, y1) with slope m is

y 2 y1

m

x 2 x1

y 2 y 1 m x 2 x1

2011 Pearson Education, Inc.

Chapter 3: Lines, Parabolas and Systems

3.1 Lines

Example 3 – Determining a Line from Two Points

Find an equation of the line passing through (−3, 8)

and (4, −2).

Solution:

2 8

10

The line has slope m 4 3 7

Using a point-slope form with (−3, 8) gives

10

y 8 x 3

7

7 y 56 10 x 30

10 x 7 y 26 0

2011 Pearson Education, Inc.

Chapter 3: Lines, Parabolas and Systems

3.1 Lines

• The slope-intercept form of an equation of the

line with slope m and y-intercept b is y mx c.

Example 5 – Find the Slope and...