8-7: parallel and perpendicular lines mr. gallo. parallel lines if two non-vertical lines have the...
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8-7: Parallel and Perpendicular Lines
Mr. Gallo
Parallel Lines If two non-vertical lines have the _________
________, then the lines are ___________.
5
4
3
2
1
-1
-2
-3
-4
-5
-6 -4 -2 2 4 6
a
b
The 2 lines to right, a and b are parallel and have a slope of 2.
What is the equation for each line?
a:
b:
same slopeparallel
2 1y x
2 2y x
Examples: Write the slope of any line that is parallel to each given line.
1). 2.) _________________
3 2y x 2 3 6x y
3mA
Bm
2
3
2
3
Point-Slope Form of an Equation:
1 1y y m x x
Where:slope
y coordinate of a given point
x coordinate of a given point
Write an equation in point-slope form for the line containing and parallel to .
1 1y y m x x
𝑚=¿ 𝑦1=¿ 𝑥1=¿¿3 4 3
1 1y y m x x
___ ___ ___y x 34 3
Write an equation in point-slope form for the line containing and parallel to 6.
1 1y y m x x
𝑚=¿ 𝑦1=¿ 𝑥1=¿¿2
3
A
B
1 3
1 1y y m x x
___ ___ ___y x 2
31 3
Write an equation in point-slope form for the line containing and parallel to 6.
1 1y y m x x
𝑚=¿¿¿ 𝑥1=¿¿4 1undefined
The original line is vertical so a vertical line with the equation would be parallel.
Perpendicular Lines If two non-vertical lines have
that are opposite , then the lines are perpendicular..
The 2 lines to right, a and b are perpendicular and have slopes of and 2 respectively.
What is the equation for each line?
a:
b:
slopesreciprocals
11
2y x
2 2y x
5
4
3
2
1
-1
-2
-3
-4
-5
-6 -4 -2 2 4 6
a
b
Examples: Write the slope of any line that is perpendicular to each given line.
1). 2.) _________________
3 2y x 2 3 6x y
1
3m
2
3m
3
2m
Write an equation in point-slope form for the line containing and perpendicular to .
1 1y y m x x
𝑚=¿ 𝑦1=¿ 𝑥1=¿¿
1
3 4 3
1 1y y m x x
___ ___ ___y x 4 3
1
3
Write an equation in point-slope form for the line containing and perpendicular to 6.
1 1y y m x x
𝑚=¿ 𝑦1=¿ 𝑥1=¿¿3
2
1 3
1 1y y m x x
___ ___ ___y x 3
2
1 3
2
3m
Write an equation in point-slope form for the line containing and perpendicular to 6.
1 1y y m x x
𝑚=¿¿¿ 𝑥1=¿¿4 1
undefined
The original line is vertical so a horizontal line with the equation would be perpendicular.
0
Homework: Reteach 8-7