Objective
The student will be able to:
find the slope of a line given 2 points and
a graph.
\
What is the meaning of this sign?
1.
2.
3.
4.
Icy Road Ahead
Steep Road Ahead
Curvy Road Ahead
Trucks Entering
Highway Ahead
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
So, what is slope???
Slope is the steepness of a line.
Slope can be expressed different ways:
( y2  y1 ) rise
vertical change
m


( x2  x1 ) run horizontal change
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.
1) Determine the slope of the line.
When given the graph, it is easier to apply
“rise over run”.
Answer:
Start with the lower point and count how
much you rise and run to get to the other
point!
6
3
rise
3
1
=
=
run
6
2
Notice the slope is positive
AND the line increases!
2) Find the slope of the line that
passes through the points (-2, -2)
and (4, 1).
USE THE
FORMULA!!
( y2  y1 )
m
( x2  x1 )
Answer:
Use the formula:
( y2  y1 )
m
( x2  x1 )
y2 is the y coordinate of the 2nd ordered pair (y2 = 1)
y1 is the y coordinate of the 1st ordered pair (y1 = -2)
(1  (2)) (1  2) 3 1
m

 
(4  (2)) (4  2) 6 2
Did you notice that Example #1 and
Example #2 were the same problem
written differently?
6
3
(-2, -2) and (4, 1)
1
slope 
2
You can do the problems either way!
Which one do you think is easiest?
3. Find the slope of the line that
passes through (3, 5) and (-1, 4).
1.
2.
3.
4.
4
-4
¼
-¼
4). Find the slope of the line that
goes through the points (-5, 3)
and (2, 1).
ANSWER:
y2  y1
m
x2  x1
1 3
m
25
1 3
m
2  (5)
2
m
7
5. Determine the slope of the line shown.
1.
2.
3.
4.
-2
-½
½
2
ANSWER
-1
2
Find points on the graph.
Use two of them and
apply rise over run.
rise 2

 2
run 1
The line is decreasing (slope is negative).
6. What is the slope of a
horizontal line?
Answer:
The line doesn’t rise!
0
m
0
number
All horizontal lines have a slope of 0.
What about a vertical slope?
The line doesn’t run!
number
m
 undefined
0
All vertical lines have an undefined slope.
Remember the word
“VUXHOY”
Vertical lines
Undefined slope
X = number; This is the equation of the line.
Horizontal lines
O - zero is the slope
Y = number; This is the equation of the line.
7. ZIPLINE!
An engineer needs to determine the slope between two points on a zipline cable in order
to evaluate the breaking power required for passengers to stop safely. A coordinate grid
has been placed over a diagram between the two points, as shown below. For estimation
purposes, a straight line between the two points can be used to find the slope. Assuming
the cable runs in a straight line, what is the slope of the line between the two points
shown? Please use the SLOPE FORMULA to show your work. Explain what the slope
‘means’ in terms of the problem (how is this will the engineer use the information)Write
your answer in complete sentences.
PRACTICE
8. What value represents the slope in the
equation: y=3x +4
9. What is the slope given the table:
X
Y
0
5
2
3
4
2
10. What is the slope between the 2 points
(3,5) and (8,4) ?
Additional Resources
• Video
http://www.virtualnerd.com/tutorials/?id=Al
g1_10_1_2 (watch the video to review how
to find the slope between 2 points)
• http://www.mathplayground.com/SaveTheZ
ogs/SaveTheZogs.html
• http://hotmath.com/hotmath_help/games/kp/
kp_hotmath_sound.swf
Additional
• http://hotmath.com/hotmath_help/games/kp/
kp_hotmath_sound.swf
• http://www.ixl.com/math/grade-8/find-theslope-of-a-graph