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1. Slope of a Line
Slope basically describes the
steepness of a line

2. Concept: What is Slope?
- SLOPE -
+SLOPE
+
Steepness
Rise
Run
Change inY
Change inX
Y=mx + b

3. Definitions of Slope
Slope is simply the change in the vertical
distance over the change in the horizontal
distance
1
2
1
2
x
x
y
y
x
y
run
rise
m
slope








The ratio of vertical change to horizontal change.
The change iny over the change inx

4. Concept: Definitions of Slope
•
•
•
The tilt or inclination of a line
The ratio of vertical change to horizontal
change.
The change iny over the change inx

5. 1
2
1
2
x
x
y
y
m



The formula above is the one which we
will use to find the slope of specific
lines
In order to use that formula we need to
know, or be able to find 2 points on the
line

6. If a line is in the form Ax + By = C,
we can use the following formula
to find the slope:
B
A
m 


7. Examples
   
 
3
1
6
2
1
5
4
6
6
,
5
,
4
,
1







m
m
3
2
5
3
2




m
y
x

8. Horizontal lines have a slope of zero
while vertical lines have no slope
Horizontal
y=
Vertical
x=
m =
0
m = no
slope

9. What does the line look like when…
• You have positive slope?
• You have negative slope?
• You have zero slope?
• You have NO slope?
(Undefined)

10. Slope = 0
Positive Slope
Negative
Slope
Negative slope is a downer
Undefined Slope
Concept: Determining Slope

11. Determine the slope of the line.
The line is decreasing (slope is
negative).
2
-1
r ise
r un

2
1
 2
Find points on the
graph.
Use two of them and
apply rise over run.

12. Slope
Mountain
Ski Resort
Positive
slope,
+ work
Negative
slope,
– work
Zero slope is
zero fun! NO slope.
Oh No!!!!
Concept: Determining Slope cont. . .

13. 1.First pick two points
on the line
The points need to be
where the lines cross
so they are integers
2. Then find therise and
run
3. Determine if the slope
of the line is positive
or negative
Rise = –2
Run = 3
r un
r ise
slope 
3
2

Concept: Determining Slope cont. . .

14. Concept: Determining Slope cont. . .
1.First pick two points
on the line
The points need to be
where the lines cross
so they are integers
2. Then find therise and
run
3. Determine if the slope
of the line is positive
or negative
Rise = 10
Run = 2
r un
r ise
slope 
2
10
 5


15. Slope= 0
Rise= 0
Run = n
Concept: Determining Slope cont. . .
Special Lines: Horizontal Lines

16. The Slope is
UNDEFINED
Rise= n
Run = 0
Concept: Determining Slope cont. . .

17. Concept: Review slope-intercept
form
Slope-Intercept Form of the Linear
Equation
y = mx + b
m
= slope
b
= y-intercept
Any linear equation which is solved
for y is in slope-intercept form.

18. Find the slope and y-intercept of
the following linear equations:
y = 3x + 4
m = 3 b = 4
y = -2x - 1
m = -2 b = -1
y = x
–
9 4
m = b =
9 4
-2 1
-2 -1
y = 5x
m = 5 b = 0
Concept: Review cont…

19. 



1: Make sure the equation is in slope-intercept
form (
y = mx +b )
2: Find the slope and y-intercept
3: Plot the y-intercept
4: Apply the slope (rise/run) to the y-intercept
Concept: Graphing Using Slope and y-Intercept

20. Concept: Graphing with slope-intercept
1.
1.
2.
1.
Start by graphing
the y-intercept (b = 2)
.
From the y-intercept,
apply “rise over run”
using your slope.
rise = 1, run = -3
Repeat this again
from your new point.
Draw a line through
your points.
1
-3
Start here
1
-3
y 
1
3
x  2
Ex:
2

21. Concept: Graphing slope-intercept cont…
They -intercept is –2, so plot
the point (0, –2) where the
line crosses the
y -axis.
The equation is already in slope-
intercept form.
SOLUTION
Graphy = x – 2
3
4
Draw a line through the two points.
The slope is , so plot a second point on the line by
moving
4 units to the right and 3 units up. This point is (4, 1).
3
4
(4, 1)
(0, – 2)
(0, – 2)
3
4
(4, 1).