SAT
Parallel lines have the same slope.
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Same slope
Parallel lines have the same slope.
Rise over run
This way is faster.
Start at the left point.
Draw a vertical line to the height of the other point.
Blue and positive means up. Red and negative means down.
From there, draw a horizontal line to the other point.
Blue and positive means forward (right). Red and negative means backwards (left).
Slope formula
You can also use the two points.
m = y₂ − y₁x₂ − x₁
Example
What is the slope of a line parallel to the line in the graph?
The dots are at (−2, 2) and (2, 0).
Parallel lines have the same slope.
Rise over run is faster.
Start at the left point, (−2, 2).
Red vertical: down −2.
Blue horizontal: forward +4.
m = riserun
m = −2+4
m = −12
Another way:
m = y₂ − y₁x₂ − x₁
m = 0 − 22 − (−2)
m = −24
m = −12
Answer: −12
Work these three in a session.
What is the slope of a line parallel to the line in the graph?
The dots are at (−1, −1) and (3, 5).
Parallel lines have the same slope.
Rise over run is faster.
Start at the left point, (−1, −1).
Blue vertical: up +6.
Blue horizontal: forward +4.
m = riserun
m = +6+4
m = 32
Another way:
m = y₂ − y₁x₂ − x₁
m = 5 − (−1)3 − (−1)
m = 64
m = 32
Answer: 32
What is the slope of a line parallel to the line in the graph?
The dots are at (−3, 1) and (1, −3).
Parallel lines have the same slope.
Rise over run is faster.
Start at the left point, (−3, 1).
Red vertical: down −4.
Blue horizontal: forward +4.
m = riserun
m = −4+4
m = −1
Another way:
m = y₂ − y₁x₂ − x₁
m = −3 − 11 − (−3)
m = −44
m = −1
Answer: −1
What is the slope of a line parallel to the line in the graph?
The dots are at (2, −1) and (4, 3).
Parallel lines have the same slope.
Rise over run is faster.
Start at the left point, (2, −1).
Blue vertical: up +4.
Blue horizontal: forward +2.
m = riserun
m = +4+2
m = 2
Another way:
m = y₂ − y₁x₂ − x₁
m = 3 − (−1)4 − 2
m = 42
m = 2
Answer: 2
Try these five on your own.
What is the slope of a line parallel to the line in the graph?
The dots are at (−3, 0) and (1, 2).
Parallel lines have the same slope.
Rise over run is faster.
Start at the left point, (−3, 0).
Blue vertical: up +2.
Blue horizontal: forward +4.
m = riserun
m = +2+4
m = 12
Another way:
m = y₂ − y₁x₂ − x₁
m = 2 − 01 − (−3)
m = 24
m = 12
Answer: 12
What is the slope of a line parallel to the line in the graph?
The dots are at (2, 4) and (4, −2).
Parallel lines have the same slope.
Rise over run is faster.
Start at the left point, (2, 4).
Red vertical: down −6.
Blue horizontal: forward +2.
m = riserun
m = −6+2
m = −3
Another way:
m = y₂ − y₁x₂ − x₁
m = −2 − 44 − 2
m = −62
m = −3
Answer: −3
What is the slope of a line parallel to the line in the graph?
The dots are at (−4, −1) and (−1, 2).
Parallel lines have the same slope.
Rise over run is faster.
Start at the left point, (−4, −1).
Blue vertical: up +3.
Blue horizontal: forward +3.
m = riserun
m = +3+3
m = 1
Another way:
m = y₂ − y₁x₂ − x₁
m = 2 − (−1)−1 − (−4)
m = 33
m = 1
Answer: 1
What is the slope of a line parallel to the line in the graph?
The dots are at (−1, 5) and (3, 2).
Parallel lines have the same slope.
Rise over run is faster.
Start at the left point, (−1, 5).
Red vertical: down −3.
Blue horizontal: forward +4.
m = riserun
m = −3+4
m = −34
Another way:
m = y₂ − y₁x₂ − x₁
m = 2 − 53 − (−1)
m = −34
Answer: −34
What is the slope of a line parallel to the line in the graph?
The dots are at (2, 0) and (5, 4).
Parallel lines have the same slope.
Rise over run is faster.
Start at the left point, (2, 0).
Blue vertical: up +4.
Blue horizontal: forward +3.
m = riserun
m = +4+3
m = 43
Another way:
m = y₂ − y₁x₂ − x₁
m = 4 − 05 − 2
m = 43
Answer: 43
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