Honors Geometry Section 3.8

Lines in the Coordinate Plane

Objectives:

1. Find the slope of the line through 2 points.

2. Find the slope of a line parallel to a given line.

3. Find the slope of a line perpendicular to a given line.

4. Write the equation of a line.

The slope of a line is a ratio that indicates how a line rises or falls

from left to right.

The slope of a nonvertical line that contains the points is

equal to the ratio

12

12

xx

yym

When graphing, it is helpful to think of slope as rise over run.

What would the slope of a vertical line be?

Why?

undefined

?

run

rise0

Examples: Find the slope of the line through the given points.

1

3

3

9

85

123

m

012

0m

7

2m

Two nonvertical lines are parallel iff their slopes are equal.

Note: Vertical lines will be parallel.

Two nonvertical lines are perpendicular iff their slopes are

opposite reciprocals.

Note: A horizontal line and a vertical line are perpendicular.

change the sign

flip the fraction

There are two forms for an equation of a line with which you should be familiar. Slope-intercept form:

Point-slope form:

bmxy

)( 11 xxmyy

Example: Write an equation in point-slope form for the line through the point (3, -5) with a slope of .

3

1

)( 11 xxmyy

)3(3

15

)3(3

15

xy

xy

Example: Write an equation, in slope-intercept form, for the line through the point (12, 5) that will be perpendicular to the line .54

3

xy

)12(5 xmy

)( 11 xxmyy

)12(3

45 xy

163

45 xy

113

4 xy

Example: Write an equation, in slope-intercept form, for the line through the points (2, -5) and (4, 2).

)4(2 xmy

)( 11 xxmyy

2

7

24

52

m

)4(2

72 xy

142

72 xy

122

7 xy