3.1The Slope of a Line

Objective:Find the slope of a line if given either the graph of the line or two points from the line.

How steep is this hill?

Is this ski slope uphill or downhill?

Definitions• Slope is a number that measures the steepness of a

line.

• Most of you are probably familiar with associating slope with the phrase "rise over run".   

• Rise means how many units you move up or down from point to point.  – On the graph that would be a change in the y values.

• Run means how far left or right you move from point to point.  – On the graph, that would mean a change of x

values.

Slope

Slope- Steepness of a line

Positive Slope Negative Slope Zero Slope No Slope

x

y

Slope:

rise (or drop) run

6

3

3

6

Triangle Method

x

y

Slope:

rise (or drop) run

6

-3

6

3

Triangle Method

x

y

Slope:

rise (or drop) run

Triangle Method

Slope Formula

21

21

xx

yym

If you are given two ordered pairs (or points) do you have to graph them to find the slope?

Examples

21

21

xx

yym

Find the slope of line that passes through the points:

a) (3, 5), (7, 12)

b) (2, 2), (9, 9)

c) (4, 5), (2, -3)

d) (-1, 5), (-4, 5)

e) (2, 7), (2, -4)

Assignment

3.1 Worksheet