The Slope of a Line

Finding Slope of a Line

• The method for finding the steepness of stairs suggests a way to find the steepness of a line.

• A line drawn from the bottom step to the top set of a set of stairs touches each step in one point.

• The rise and the run of a step are the vertical and the horizontal changes, respectively, between two points on the line.

Finding the Slope of a Line

• The steepness of the line is the ratio of rise to run, or vertical change to horizontal change, for this step.

• We call the steepness of a line its slope.

Important things about slope…

•Slope is the change in y over change in x.

•Slope is represented by the letter m

•Vertical line has NO slope (undefined)

•Horizontal line has a slope zero (0)

Formula for slope:

12

12

xx

yym

Find the slope of a line passing through points (-2,4) and (3,6)

m =

6 - 43 - -

2

= 25

m =

4 - 6-2 - 3

= -2-5

25=

or

Find the slope of a line passing through points (1,1)

and (3,-2)

31

21

m

2

3

= - 32

A slope of -3/2 means that or every time y goes down 3, x moves over 2

Graph and count to check.

Classify lines by their slope:

1. A line with a positive slope rises from left to right (m>0)

x

y

2. A line with a negative slope falls down from left to right

(m<0)

x

y

3. A line with a zero slope is horizontal (m=0) Equation y = 3

x

y

4. A line with an undefined slope is vertical (m is undefined) YOU

CANT DIVIDE BY 0!

x

y

Find the slope by using the graph.

1234

-4-3

-2

-1-4 -3 -2-1 1 2 3 4

To find the slope, start with one point and count up how many rows it goes up and count how many rows it goes over. Make this a fraction and reduce if necessary.

This line goes up 2 and over 1.

The slope is 2/1 or 2.

Find the slope by using the graph.

1234

-4-3

-2

-1-4 -3 -2-1 1 2 3 4

To find the slope, start with one point and count up how many rows it goes up and count how many rows it goes over. Make this a fraction and reduce if necessary.This line goes down

2 and over 1.

The slope is -2/1 or -2.