honors geometry section 3.8 lines in the coordinate plane
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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
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