The Slope of a Line

Finding the Change with Growth Triangles

What is the growth factor for this line?

11

1

99

927

Change3

9

1

9

Change in y direction

Change in x direction

Slope of a LineThe 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.

y

x

“Delta y”=

Change in y“Delta x”

=Change in x

Example: What is the slope of the line?

= 4

= 2Slope y

x 2

4 12

What is the equation of the line?12 2y x

Slope Triangle

Slope-Intercept Form

33

2y x

First plot the y-intercept on

the y-axis

Next, use rise over run to plot new points

Now connect the points with a line!

You can go backwards if you need!

Graph:

Steepness of a Line

What makes a line steeper?

y x 3

y 5x 3The slope is further

away from 0.

14 3y x

The slope is closer to 0.

What makes a line less steep?

Different Values of Slope

Negative Zero Positive

y :

x :

y :

x :

y :

x :

Decreasing Horizontal Increasing

Negative

Positive

Zero

Positive

Positive

Positive

Always “run” to the right

Parallel Lines

The slopes of parallel lines are

Example:

y 2x 3

y 2x 6

equal....

The rate of change of

parallel lines is the

same.

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.

Slopeyx

y0

undefined

...

The graph is not changing in the

x-direction You can not divide by 0.

2 1

2 1

y yy

x x x

Slope Formula

The slope of the line through the points (x1, y1) and (x2, y2) is given by:

Ex: Find the slope between (2, -14) and (10,30)

448 11

230 14 yx

10 2