Lesson 4-4 Parallel And Perpendicular Lines Math Worksheet
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1
2
3
4
5
6
7Parallel and Perpendicular Lines
Why?
Why?
Notice the squares, rectangles
Then
Then
and lines in the piece of art shown
You wrote equations
at the right. Some of the lines
in slope-intercept
intersect forming right angles.
form.
(Lesson 4-2)
Other lines do not intersect
Now
Now
at all.
Write an equation of
the line that passes
through a given point,
Parallel Lines
parallel to a given line.
Lines in the same plane that do not intersect are called parallel lines.
Write an equation of
Parallel lines have the same slope.
the lines that passes
through a given point,
y
perpendicular to a
All vertical lines
given line.
are parallel.
New Vocabulary
New Vocabulary
If two nonvertical lines
in a plane have the
parallel lines
same slope, then they
perpendicular lines
are parallel.
x
Math Online
Extra Examples
You can write an equation of a line parallel to a given line if you know a point
Personal Tutor
Self-Check Quiz
on the line and an equation of the given line. First find the slope of the given line.
Homework Help
Then, substitute the point provided and the slope from the given line into the
point-slope form.
EXAMPLE 1
Parallel Line Through a Given Point
Write an equation in slope-intercept form for the line that passes through
( -3, 5 ) and is parallel to the graph of y = 2x - 4.
Step 1
The slope of the line with equation y = 2x - 4 is 2. The line parallel to
y = 2x - 4 has the same slope, 2.
Step 2
Find the equation in slope-intercept form.
y -
y
= m(x -
x
)
Point-slope form
1
1
y -
5
= 2[x - (-3)]
Replace m with 2 and ( x
, y
) with ( -3, 5 ) .
1
1
y - 5 = 2 ( x + 3 )
Simplify.
y - 5 = 2x + 6
Distributive Property
y - 5
+ 5
= 2x + 6
+ 5
Add 5 to each side.
y = 2x + 11
Write the equation in slope-intercept form.
Check Your Progress
(
)
1. Write an equation in point-slope form for the line that passes through
4, -1
_
1
and is parallel to the graph of y =
x + 7.
4
Personal Tutor
237
Lesson 4-4 Parallel and Perpendicular Lines
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