Sullivan Precalculus: Section 1'3: Lines

1
Sullivan Precalculus Section 1.3 Lines

• Objectives
• Calculate and Interpret the Slope of a Line
• Graph Lines Given a Point and the Slope
• Use the Point-Slope Form of a Line
• Find the Equation of a Line Given Two Points
• Write the Equation of a Line in Slope-Intercept
  Form
• Define Parallel and Perpendicular Lines
• Find Equations of Parallel Lines
• Find Equations of Perpendicular Lines

2
Let and be two
distinct points with . The slope m of
the non-vertical line L containing P and Q is
defined by the formula
If , L is a vertical line and the
slope m of L is undefined (since this results in
division by 0).
3
Slope can be though of as the ratio of the
vertical change ( ) to the
horizontal change ( ), often termed
rise over run.
x
4
(No Transcript)
5
1
Find the slope of the line containing the points
(-1, 4) and (2, -3).
6
Compute the slopes of the lines L1, L2, L3, and
L4 containing the following pairs of points.
Graph all four lines on the same set of
coordinate axes.
7
(No Transcript)
8
If , then is zero and
the slope is undefined. Plotting the two points
results in the graph of a vertical line with the
equation .

L
y
x
9
Example 2 Draw the graph of the equation x 2.
y
x 2
x
10
Example 3 Draw the graph of the line passing
through (1,4) with a slope of -3/2.
Step 1 Plot the given point. Step 2 Use the
slope to find another point on the line (vertical
change -3, horizontal change 2).
y
2
(1,4)
-3
(3,1)
x
11
Theorem Point-Slope Form of an Equation of a Line
An equation of a non-vertical line of slope m
that passes through the point (x1, y1) is
12
Example Find an equation of a line with slope -2
passing through (-1,5).
13
A horizontal line is given by an equation of the
form y b, where (0,b) is the y-intercept.
Example Graph and write out the equation of the
line that goes through the point (2,4) and is
parallel to the x-axis.
y 4
14
Point-Slope Form of an Equation of a Line

• Can be used to form an equation of a line when
  you know the SLOPE of the line and a POINT on the
  line.

15
1. Can be used to form a line 2. Can be used to
find the SLOPE and y-intercept of a line
16
Example Find the slope m and y-intercept (0,b)
of the graph of the line 3x - 2y 6 0.
17
Example Find an equation of the line L
containing the points (-1, 4) and (3, -1) by
using two of the forms above.
18
Definitions Parallel Lines
Two lines are said to be parallel if they do not
have any points in common.
Two distinct non-vertical lines are parallel if
and only if they have the same slope and have
different y-intercepts.
19
Definitions Perpendicular Lines
Two lines are said to be perpendicular if they
intersect at a right angle.
Two non-vertical lines are perpendicular if and
only if the product of their slopes is -1.
20
Example Find the equation of the line
perpendicular to y -3x 5 passing through
(1,5).
Slope of perpendicular line
21
Section 1.3 Assignment

• Section 1.3 Assignment
• 1-10ALL, 13, 23-29Odd, 33, 37-43Odd, 51-67Odd,
  77, 83, 85, 91, 99, 101, 102,