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ObjectiveThe student will be able to:
find the slope of a line given 2 points and
a graph.
Designed by S.Tyler, VHS; V.Hiner, GHS; L.Gilkey MPMS
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What is the meaning of this sign?
1. Icy Road Ahead
2. Steep Road Ahead
3. Curvy Road Ahead
4. Trucks Entering
Highway Ahead
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What does the 7% mean?
7% is the slope of the road.
It means the road drops 7 feet
vertically for every 100 feet
horizontally.
7% 7 feet
100 feet
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Slope:
A line has a positive slope if it is
going uphill from left to right.
A line has a negative slope if it is
going downhill from left to right.
Is a measure of the steepness of a line, or a section
of line, connecting two points.
If the slope is a constant rate of change, the line is
linear.
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Slope can be expressed different ways:
2 1
2 1
( ) vertical change
( ) horizontal change
y y risem
x x run
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Tell if the following slopes go up or
down (left to right).
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When given the graph, it is easier to apply
“rise over run”.
1) Determine the slope of the line.
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Start with the lower point and count how
much you rise and run to get to the other
point!
Determine the slope of the line.
6
3
run
3
6= =
1
2
rise
Notice the slope is positive
AND the line increases!
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Start with the upper point and count how
much you rise and run to get to the other
point!
Determine the slope of the line.
-6
-3
run
-3
-6= =
1
2
rise
It does not matter which
point you start with,
direction indicates the sign.
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2) Find the slope of the line that passes
through the points (-2, -2) and (4, 1).
(1 ( 2))
(4 ( 2))m
(1 2)
(4 2)
When given points, it is easier to use the formula!
y2 is the y coordinate of the 2nd ordered pair (y2 = 1)
y1 is the y coordinate of the 1st ordered pair (y1 = -2)
13
6 2
2 1
2 1
( )
( )
y ym
x x
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Did you notice that Example #1 and
Example #2 were the same problem
written differently?
(-2, -2) and (4, 1)6
31
2slope
You can do the problems either way!
Which one do you think is easiest?
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3) Find the slope of the line that goes
through the points (-5, 3) and (2, 1).
m y2 y1
x2 x1
1 3
2 ( 5)m
1 3
2 5m
2
7m
x1 y1 x2 y2
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Example 4) Find the slope of the line
that passes through (3, 5) and (-1, 4).
1. 4
2. -4
3. ¼
4. - ¼
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You Try:
1. (3, 5) , (1, 4)
1. -2
2. -1/2
3. 2
4. 1/2
2. (5, -3), (2, 1)
1. 3/4
2. -4/3
3. -3/4
4. 4/3
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Determine the slope of the line.
The line is decreasing (slope is negative).
2
-1
rise
run
2
1 2
Find points on the graph.
Use two of them and
apply rise over run.
OR
-2
1
rise
run
-2
1 2
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Example 5:
What is the slope of a horizontal line?
Horizontal lines do not rise!
m 0
number 0
All horizontal lines have a slope of 0.
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Example 6:
What is the slope of a vertical line?
Vertical lines do not run!
All vertical lines have an undefined slope.
m number
0 undefined
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1
Example 7:
Draw a line through the point (2,0)
that has a slope of 3.
1. Graph the ordered pair (2, 0).
2. From (2, 0), apply rise over
run (write 3 as a fraction).
3. Plot a point at this location.
4. Repeat rise over run from
new point
5. Draw a straight line through
the points.
3
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You Try:
1. Point = (-2, 4)
and slope = -2/3
2. Point = (0, -4)
and slope = 0
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The slope of a line that goes through
the points (r, 6) and (4, 2) is 4. Find r.
To solve this, plug the given
information into the formula
m ( y
2 y
1)
(x2 x
1)
.
2 64
4 r
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4 4
1 4 r
To solve for r, simplify and write as
a proportion.
4 4
1 4 r
2 64
4 r
Cross multiply.
1(-4) = 4(4 – r)
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Simplify and solve the equation.
1(-4) = 4(4 – r)
-4 = 16 – 4r
-16 -16
-20 = -4r
-4 -45 = r
The ordered pairs are (5, 6) and (4, 2)
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You Try:
1. m = -3/2 and
goes through
(r,6) and (10,-3)
1. 12
2. 8
3. 4
4. -4
2. m = 3/4 and
goes through (3,4)
and (-1,r)
1. 9
2. 1
3. -7
4. 5