2.6 Extension Writing Equations of Parallel and Perpendicular Lines.
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Transcript of 2.6 Extension Writing Equations of Parallel and Perpendicular Lines.
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