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...