the slope of a line. finding slope of a line the method for finding the steepness of stairs suggests...
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The Slope of a Line
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Finding Slope of a Line
• The method for finding the steepness of stairs suggests a way to find the steepness of a line.
• A line drawn from the bottom step to the top set of a set of stairs touches each step in one point.
• The rise and the run of a step are the vertical and the horizontal changes, respectively, between two points on the line.
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Finding the Slope of a Line
• The steepness of the line is the ratio of rise to run, or vertical change to horizontal change, for this step.
• We call the steepness of a line its slope.
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Important things about slope…
•Slope is the change in y over change in x.
•Slope is represented by the letter m
•Vertical line has NO slope (undefined)
•Horizontal line has a slope zero (0)
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Formula for slope:
12
12
xx
yym
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Find the slope of a line passing through points (-2,4) and (3,6)
m =
6 - 43 - -
2
= 25
m =
4 - 6-2 - 3
= -2-5
25=
or
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Find the slope of a line passing through points (1,1)
and (3,-2)
31
21
m
2
3
= - 32
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A slope of -3/2 means that or every time y goes down 3, x moves over 2
Graph and count to check.
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Classify lines by their slope:
1. A line with a positive slope rises from left to right (m>0)
x
y
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2. A line with a negative slope falls down from left to right
(m<0)
x
y
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3. A line with a zero slope is horizontal (m=0) Equation y = 3
x
y
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4. A line with an undefined slope is vertical (m is undefined) YOU
CANT DIVIDE BY 0!
x
y
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Find the slope by using the graph.
1234
-4-3
-2
-1-4 -3 -2-1 1 2 3 4
To find the slope, start with one point and count up how many rows it goes up and count how many rows it goes over. Make this a fraction and reduce if necessary.
This line goes up 2 and over 1.
The slope is 2/1 or 2.
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Find the slope by using the graph.
1234
-4-3
-2
-1-4 -3 -2-1 1 2 3 4
To find the slope, start with one point and count up how many rows it goes up and count how many rows it goes over. Make this a fraction and reduce if necessary.This line goes down
2 and over 1.
The slope is -2/1 or -2.