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The slope is the level of steepness of a line. It explains the rate of change of a linear line.
Anchor 1
The symbol of the slope is notated as 'm'.
It is the slant of the line and explains its' direction.
The direction can be pos., neg, or a constant line.
It measures the steepness of a line.
This explains the rise and fall of a straight line.
It is measured by dividing the change in the y-value by the change in the x-value.
SLOPE FORMULA
Components of the slope formula
m =
1
y + y
2
1
x + x
2
=
rise
run
=
change of y
change of x
Slope Formula
Example of the components of the slope formula
What is point A:
(4, 6):
x = 4
y = 6
1
1
What is point B:
(3, 2):
2
x = 3
y = 2
2
What is the slope?
m =
1
y - y
2
1
x - x
2
2
3
(x - x ) = run
1
2
4
5
1
2
(y - y ) = rise
(4, 6)
A
The slope rises
vertical (y)
(+ 4) units .
1
2
B
(3, 2)
The slope runs horizontal (x)
(+ 1) units .
8
6
4
Substitute point A and B into the slope formula:
Point A: (4, 6)
Point B: (3, 2)
m =
2 - 6
3 - 4
=
-4
-1
=
4
4-SLOPE TYPES
Visually describes the four different common slopes
Positive Slope
4
3
2
1
1
2
3
4
Slope is pos., upward and increasing
x increases, y increases
Negative Slope
4
1
3
2
1
2
3
4
Slope is neg., downward and decreasing
x increases, y decreases
Undefined Slope
1
3
2
4
1
2
3
4
Slope is constant vertical
Slope is undefined
x constant, y increases
Zero Slope
1
4
3
2
1
2
3
4
Slope is constant horizontal
Slope is always 0
x increases, y constant
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