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2.6 ExtensionWriting Equations of
Parallel and Perpendicular Lines
“parallel”
Parallel Lines• Parallel lines have the same exact slope
(“m”) and a different y-intercept (“b”).
•y = 2x +3 and y = 2x +11 are parallel.
• All vertical lines are parallel.
• All Horizontal lines are parallel
y=2 and y =-1 are parallel
x = -5 and x = 9 are parallel.
Determine if the lines are parallel
and1
4 3
x x Y
All vertical lines are parallel.
Determine if the lines are parallel
an2 d11 2 2y x y x
N
1
2
11
2y x
2 2y x
Determine if the lines are parallel
and3 5 5 15 10x y y x
Y
3 5y x 3 2y x 3 5 y x 5 15 10y x
Steps to write an equation of a line that passes through the given point
and parallel to the given line
1.) Identify a parallel slope to the line
2.) Either use slope- intercept or point slope form to write your equation
Write an equation of a line that passes through the given point and parallel to the given line
( 2,1); 3 4y x ( 2,1); 3m
1 3( ( 2))y x 1 3( 2)y x
1 3 6y x 1 1
3 7y x
Perpendicularmeans “at right angles”
All three red lines are perpendicular to the green line.
Slope and Line relationships• Perpendicular lines (): have the
opposite reciprocal slopes•y = 2x + 3 and y =
are perpendicular.
• If you multiply two perpendicular slopes your product will be -1
• All vertical and horizontal lines are perpendicular
6x 1
-2
2 11
1 2
Determine if the lines are perpendicular:
and9 7
1 77 9
y x y x
Y
Determine if the lines are perpendicular:
and7 8
4 78 7
y x y x
NOne must be
positive;
the other negative.
Determine if the lines are perpendicular:
and2 3y x Y
Steps to write an equation of a line that passes through the given point and perpendicular to the given line
1.) Identify a perpendicular slope to the line
2.) Either use slope- intercept or point slope form to write your equation
Write an equation of a line that passes through the given point and perpendicular to the given line
1(4,2); 1
3y x
(4,2); 3m2 3( 4)y x 2 3 12y x 2 2
3 10y x
Homework
RPJ: Page 49-50 (1-16) all
