The Slope of a Line
Finding the Change with Growth
Triangles
What is the growth factor for this line?
Change in y direction
9
91
9 1
1
27
Change 
3
Change in x direction
9

1
9
Slope of a Line
The slope is a measure of steepness. It is the ratio of the
vertical change to the horizontal change OR the ratio of
the change in y to the corresponding change in x.
“Delta y”
=
Change in y
Example:
y
x
Slope Triangle
What is the slope of the line?
=2
=4
“Delta x”
=
Change in x
Slope  yx 
2
4

1
2
What is the equation of the line?
y  12 x  2
Slope-Intercept Form
Graph:
3
y  x 3
2
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Steepness of a Line
y  x3
What makes a
line steeper?
What makes a
line less steep?
y  5x  3
y  x3
The slope is further
away from 0.
The slope is closer
to 0.
1
4
Different Values of Slope
Negative
Zero
Positive
Decreasing
Horizontal
Increasing
y : Negative
x : Positive
y :
Zero
Always “run” to the right
Positive
x :
y : Positive
x : Positive
Parallel Lines
The slopes of parallel lines are...
equal.
Example:
y  2x  3
The rate of
change of
parallel
lines is the
same.
y  2x  6

NOTE: The parallel lines can NOT have the same y-intercept.
Or else they would intersect all of the time since they would
be the same line.

Vertical Lines
The slope of a vertical line is ...
undefined.
Example: Find the slope of the line below.
The graph is not
changing in the
x-direction
Slope 
You can not divide
by 0.
y
x

y
0
 undefined
Slope Formula
The slope of the line through the points (x1, y1)
and (x2, y2) is given by:
y y2  y1

x x2  x1
Ex: Find the slope between (2, -14) and (10,30)
y
x

30  14
10  2

44
8

11
2