EXAMPLE 1 Finding Slope

The Mount Pilatus Railway in the Swiss Alps is the steepest cogwheel railway in the world. The track rises about 20 feet vertically for every 50 feet it runs horizontally. How can you describe the steepness of the track?

Cogwheel Railway

EXAMPLE 1 Finding Slope

The diagram shows the rise and the run of the Mount Pilatus Railway described above.

slope = runrise

= 50 ft20 ft 2

5=

ANSWER

The track has a slope of .25

5

2

GUIDED PRACTICE for Example 1

slope = runrise 1

3=

ANSWER

The track has a slope of .13

3

1

1. Using slope, describe the steepness of a ramp that rises 6 feet vertically for every 18 feet it reaches horizontally.

Ramps

= 18 ft6 ft

EXAMPLE 2 Positive and Negative Slope

Find the slope of the line.

m = runrise

=y2 – y1x2 – x1

= 7 – 25 – 1

54

=

m = runrise

=y2 – y1x2 – x1

= 3 – 64 – 2

–32

= 32

or –

EXAMPLE 3 Zero and Undefined Slope

Find the slope of the line.

m = runrise

=y2 – y1x2 – x1

= 3 – 36 – 2

04

=

=y2 – y1x2 – x1

4 – (–2)1 – 1=

0= The slope is undefined

m = runrise

= 60

GUIDED PRACTICE for Examples 2 and 3

Find the slope of the line passing through the points.

2. (2, 1), (6, 4)

m = runrise

= 4 – 16 – 2

34

=

3. (0, 6), (10, 0)

m = runrise

=y2 – y1x2 – x1

= 0 – 610 – 0 10

= –6

4. (– 3, – 4), (5, 2)

m = runrise

=y2 – y1x2 – x1 4

= 3= 2 – (–4)5 – (–3)

=y2 – y1x2 – x1

5= –3

GUIDED PRACTICE for Examples 2 and 3

m = runrise

=y2 – y1x2 – x1

0=

6. (1, 6), (1, 2)

m = runrise

=y2 – y1x2 – x1

= 2 – 61 – 1

7. (– 8, 3), (8, 3)

m = runrise

=y2 – y1x2 – x1

= 3 – 38 – (–8)

5. (1, 5), (– 3, 5)

= 0

= – 40

undefined

= 5 – 5–3 – 1