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1.
SLOPE OF A LINE
When you hear the word
“slope”
what comes to mind?
2.
Slope of a Line
The slope of a line measures the steepness of a line. You
have probably heard teachers say “rise over run”.
• Rise means how many units you move up or down from
point to point. On a graph that would be a change in the
y-values.
• Run means how many units you move left or right from
point to point. On a graph that would be a change in the
x-values.
rise
slope run
c
3.
Positive Slope
Note that a line y=0.5x+3
6
with a positive 5
slope increases as 4
3
you read the 2
graph from left to 1
0
right. -6 -4 -2 0 2 4 6
Slope-Intercept Form
c
4.
Negative Slope
y=-3x-2
6
Note that a line 4
with a negative 2
slope decreases as -3 -2 -1
0
0 1 2 3
-2
you read the
-4
graph from left to -6
right -8
-10
Slope-Intercept Form
c
5.
Zero Slope
y=0x+1
Note that a line 1.2
with a slope of 1
zero is horizontal 0.8
0.6
as you read the
0.4
graph from left to 0.2
right 0
-3 -2 -1 0 1 2 3
Slope-Intercept Form
c
6.
Undefined Slope
X = -2 5
When a line is 4
vertical, the slope is 3
undefined. A 2
vertical line cannot 1
be written in Slope- 0
-2.5 -2 -1.5 -1 -0.5 0
Intercept Form. -1
-2
-3
c
7.
Slope Formula Given Two Points
You are now going to calculate the slope of a
line and compare it to the Slope-Intercept
Equations on the four previous slides. Given
two points, x y and x y , calculate the slope.
1, 1 2
, 2
m = rise = change in y = x 2 - y1
run change in x
y
- x1
2
c
8.
Positive Slope Given Two Points:
A= - 4,1 B= 2,4
m = 4 - 1 = 3 = 1 = 0.5
2 - -4 6 2
Note that the slope of the line passing through
points A and B is 0.5. Compare this to the first
graph by clicking the arrow.
9.
Negative Slope Given Two Points:
A= - 2,4 B= 1,-5
m = -5 - 4 = -9 = -3
1 - -2 3
Note that the slope of the line passing through
points A and B is -3. Compare this to the second
graph by clicking the arrow.
10.
Zero Slope Given Two Points:
A= - 2,1 B= 2,1
m = 1- 1 = 0 = 0
2 - -2 4
Note that the slope of the line passing through
points A and B is 0. Compare this to the third
graph by clicking the arrow.
11.
Undefined Slope Given Two Points:
A= - 2,4 B= 4,-7
m= -2 - 4 = -6 = undefined
-2 - -2 0
Note that the slope of the line passing through points
A and B is undefined. Compare this to the fourth
graph by clicking the arrow.
12.
Checking for Understanding
The Slope-Intercept Form of a line is
y=mx+b where m is the slope of the line
and b is the y-intercept of the line. Did
you notice the relationship between the
slopes that were calculated and the
graphs of the equations? Now continue
with the practice problems.
13.
Practice Problems
Given the equation, what is
the slope of the line?
y 2x 7
A) 7 C) 3 3
2
B) 2 D) X
3
14.
That response is incorrect, the correct
2
response is 3 . Remember that when
an equation is in Slope-Intercept
form, y=mx+b, the slope is the
coefficient of x. Don’t be discouraged!
Let’s try another problem.
16.
Practice Problems
Calculate the slope of the line that passes
through the given points.
A= -5,2 A) -1 C) 5
B= 4,-7
B) 5 D) 9
9 5
17.
That is incorrect. The correct response is A.
Refer back to slide 9 if you need to review
how to calculate the slope of a line using
the slope formula.
-7 - 2 -9
m= = = -1
4 - -5 9
21.
That is incorrect. If you start at the point
(0,-3) and move to the point(1,-1), the
movement was 2 units up and 1 unit right
which means the slope is 2 which is 2.
1
22.
Conclusion
Today you have learned to find the slope
of a line by reading a graph, using the
slope formula, and by knowing that in the
slope-intercept formula, m is the slope.
In our next lesson, we will continue our
study of linear functions. Cheers!
23.
Positive Slope
Note that a line y=0.5x+3
6
with a positive 5
slope increases as 4
3
you read the 2
graph from left to 1
0
right. -6 -4 -2 0 2 4 6
Slope-Intercept Form
24.
Negative Slope
y=-3x-2
6
Note that a line 4
with a negative 2
slope decreases as -3 -2 -1
0
0 1 2 3
-2
you read the
-4
graph from left to -6
right -8
-10
Slope-Intercept Form
25.
Zero Slope
y=0x+1
Note that a line 1.2
with a slope of 1
zero is horizontal 0.8
0.6
as you read the
0.4
graph from left to 0.2
right 0
-3 -2 -1 0 1 2 3
Slope-Intercept Form
26.
Undefined Slope
X = -2 5
When a line is 4
vertical, the slope is 3
undefined. A 2
vertical line cannot 1
0
be written in Slope- -2.5 -2 -1.5 -1 -0.5 0
-1
Intercept Form.
-2
-3