Parallel And Perpendicular Lines Worksheet Page 23
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50Study Tip
Slope and a Point
Example
Example
2
2
1
Choosing Forms
Write an equation in point-slope form of the line whose slope is
that
2
of Linear
contains (3,
7).
Equations
y
y
m(x
x
)
Point-slope form
If you are given a point
1
1
1
on a line and the slope
1
y
( 7)
(x
3)
m
, (x
, y
)
(3,
7)
1
1
2
2
of the line, use point-slope
form. Otherwise, use
1
y
7
(x
3)
Simplify.
slope-intercept form.
2
1
The point-slope form of the equation of the line is y
7
(x
3).
2
Both the slope-intercept form and the point-slope form require the slope of a line
in order to write an equation. There are occasions when the slope of a line is not
given. In cases such as these, use two points on the line to calculate the slope. Then
use the point-slope form to write an equation.
Study Tip
Two Points
Example
Example
3
3
Writing Equations
Write an equation in slope-intercept form for line .
Note that the point-slope
Find the slope of
by using A( 1, 6) and B(3, 2).
y
form of an equation is
y
y
A ( 1,
)
6
different for each point
2
1
m
Slope formula
x
x
used. However, the slope-
2
1
intercept form of an
2
6
B ( 3,
)
2
x
1, x
3, y
6, y
2
equation is unique.
1
2
1
2
3
(
1)
4
or
1
Simplify.
x
O
4
Now use the point-slope form and either point
to write an equation.
Using Point A:
y
y
m(x
x
)
Point-slope form
1
1
y
6
1[x
(
1)]
m
1, (x
, y
)
( 1, 6)
1
1
y
6
1(x
1)
Simplify.
y
6
x
1
Distributive Property
y
x
5
Add 6 to each side.
Using Point B:
y
y
m(x
x
)
Point-slope form
1
1
y
2
1(x
3)
m
1, (x
, y
)
(3, 2)
1
1
y
2
x
3
Distributive Property
y
x
5
Add 2 to each side.
One Point and an Equation
Example
Example
4
4
Write an equation in slope-intercept form for a line containing (2, 0) that is
perpendicular to the line y
x
5.
Since the slope of the line y
x
5 is
1, the slope of a line perpendicular to it is 1.
y
y
m(x
x
)
Point-slope form
1
1
y
0
1(x
2)
m
1, (x
, y
)
(2, 0)
1
1
y
x
2
Distributive Property
146 Chapter 3 Parallel and Perpendicular Lines
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