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EXAMPLE 5

Roller Coasters. During the climb on the Magnum XL- 200 roller coaster, you move 41 feet upward for every 80 feet you move horizontally. At the crest of the hill, you have moved 400 feet forward.

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EXAMPLE 5

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  1. Roller Coasters During the climb on the Magnum XL-200 roller coaster, you move 41feet upward for every 80feet you move horizontally. At the crest of the hill, you have moved 400feet forward. Making a Table: Make a table showing the height of the Magnum at every 80feet it moves horizontally. How high is the roller coaster at the top of its climb? a. EXAMPLE 5 Solve a real-world problem

  2. Calculating : Write a fraction that represents the height the Magnum climbs for each foot it moves horizontally. What does the numerator represent? b. Using a Graph: Another roller coaster, the Millennium Force, climbs at a slope of 1. At its crest, the horizontal distance from the starting point is 310feet. Compare this climb to that of the Magnum. Which climb is steeper? c. EXAMPLE 5 Solve a real-world problem

  3. a. rise Slope of the Magnum b. = = = = run 41 80 41 80 80 80 0.5125 1 EXAMPLE 5 Solve a real-world problem SOLUTION The Magnum XL-200 is 205 feet high at the top of its climb. The numerator, 0.5125, represents the slope in decimal form.

  4. Use a graph to compare the climbs. Let xbe the horizontal distance and let ybe the height. Because the slope of the Millennium Force is 1, the rise is equal to the run. So the highest point must be at (310,310). c. ANSWER The graph shows that the Millennium Force has a steeper climb, because the slope of its line is greater (1 > 0.5125). EXAMPLE 5 Solve a real-world problem

  5. Line qpasses through the points (0, 0) and (– 4, 5). Line tpasses through the points (0, 0) and (–10, 7). Which line is steeper, qort ? 0 – 5 – 5 – 7 q – 0.7 – 1.25 = = = = = 0 – (– 4) 4 0 – 7 t = 0 – (– 10) 10 for Example 5 GUIDED PRACTICE SOLUTION Find the slope of q Find the slope of t Line q is steeper than line t.

  6. What If?Suppose a roller coaster climbed 300feet upward for every 350feet it moved horizontally. Is it more steep or less steep than the Magnum? than the Millenium Force? 300 0.85714 = = 350 for Example 5 GUIDED PRACTICE SOLUTION Slope of roller coaster The roller coaster is more steep than Magnum as its slope is greater. The roller coaster is less steep than Millenium Force as its slope is less.

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