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 = run rise = 50 ft 20 ft 2 5 = ANSWER The track has a slope of

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

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

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

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

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