1. Monday, October 18
Slope of a Line
LF.2.AC.5: Calculate the slope given two points, a graph of a line, or an equation of a line

2. The Slope of a Line
The slope of a line is a number that describes the steepness of a line. Any two numbers on the line can be used to determine the slope. x y
The rise is the difference in the y-values of the two points.
The run is the difference in the x-values of the two points.
The slope is the ratio
of rise to run, usually written this way:
Run is +2
Rise is +3
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Slope of a Line

3. Finding the Slope of a Line
You may choose any two points on the line to find the slope.
Start with the point on the left, and move to the other point.
From A count up (+2) and over 3 (+3)
So the slope is x y B A
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Slope of a Line

4. Finding the Slope of a Line
What is the slope of CD?
Start with point C and move to point D.
Move down 3 (-3) and over 1 (+1).
The slope is x y C D
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Slope of a Line

5. Slope Formula
The formula for the slope m of a line containing the points (x1, y1) and (x2, y2).
Remember that if the line slants upwards from left to right the slope is positive.
If it slants downwards, the slope is negative.
A horizontal line has a slope of 0.
A vertical line has no slope or the slope
is undefined.
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Slope of a Line

6. Example 1: Finding the Slope
Use the slope formula to determine the slope of each line.
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Slope of a Line

7. Parallel and Perpendicular Lines
Parallel Lines
Two parallel lines have the same slope. Any two vertical lines are parallel.
Perpendicular Lines
Two perpendicular lines have slopes that are the opposite reciprocal of each other. Vertical and horizontal lines are perpendicular to each other.
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Slope of a Line

8. Examples
Find the slope of the line passing through these two points (3, 5) and (-1, -2)
The slope of a line parallel to the line above would be
The slope of a line perpendicular to this
line would be
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Slope of a Line