# Managerial

## Managerial

INTRODUCTORY MATHEMATICAL
ANALYSIS
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
3.4) 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...