EXAMPLE 1

2. Cogwheel Railway The Mount Pilatus Railway in the Swiss Alps is the steepest cogwheel railway in the world. The track rises about 20feet vertically for every 50feet it runs horizontally. How can you describe the steepness of the track? EXAMPLE 1 Finding Slope

3. 2 20 ft rise 2 = = slope = 50 ft run 5 5 ANSWER 2 The track has a slope of . 5 EXAMPLE 1 Finding Slope The diagram shows the rise and the run of the Mount Pilatus Railway described above.

4. 1. Using slope, describe the steepness of a ramp that rises 6 feet vertically for every 18 feet it reaches horizontally. Ramps 6 ft rise 1 = slope = 1 18 ft run 3 = 3 ANSWER 1 The track has a slope of . 3 for Example 1 GUIDED PRACTICE

5. y2 – y1 y2 – y1 rise rise = = m= m= x2 – x1 x2 – x1 run run 7 – 2 3 – 6 = = 5 – 1 4 – 2 5 –3 3 = = or – 4 2 2 EXAMPLE 2 Positive and Negative Slope Find the slope of the line.

6. y2 – y1 y2 – y1 rise rise = = m= m= x2 – x1 x2 – x1 run run 3 – 3 4 – (–2) = = 6 – 2 1 – 1 0 6 = = 4 0 0 = EXAMPLE 3 Zero and Undefined Slope Find the slope of the line. The slope is undefined

7. y2 – y1 rise 4 – 1 3 = = = m= x2 – x1 6 – 2 run 4 y2 – y1 rise –3 –6 0 – 6 = = = = m= x2 – x1 10 – 0 run 5 10 y2 – y1 rise 2 – (–4) 3 = = = m= x2 – x1 run 5 – (–3) 4 for Examples 2 and 3 GUIDED PRACTICE Find the slope of the line passing through the points. 2. (2, 1), (6, 4) 3. (0, 6), (10, 0) 4. (–3, – 4), (5, 2)

8. y2 – y1 rise 5 – 5 0 = = = m= x2 – x1 run –3 – 1 y2 – y1 rise 2 – 6 – 4 = = = m= x2 – x1 1 – 1 run 0 y2 – y1 rise 3 – 3 0 = = = m= x2 – x1 run 8 – (–8) for Examples 2 and 3 GUIDED PRACTICE 5. (1, 5), (– 3, 5) 6. (1, 6), (1, 2) undefined 7. (–8, 3), (8, 3)