Section 3.3 Slope of a Line and Rate of Change 237 By visual inspection, Mt. Dora Trail is “steeper” than Park Trail. To measure the slope of a line quantitatively, consider two points on the line. The slope of the line is the ratio of the vertical change (change in y) between the two points and the horizontal change (change in x). As a memory device, we might think of the slope of a line as “rise over run.” See Figure 3-15. Change in x (run) To move from point A to point B on To move from point A to point B on Park Trail, rise 2 ft and move Mt. Dora Trail, rise 12 ft and move to the right 6 ft (Figure 3-16). to the right 6 ft (Figure 3-17). Figure 3-16 Figure 3-17 change in y change in x The slope of Mt. Dora Trail is greater than the slope of Park Trail, confirming the observation that Mt. Dora Trail is steeper. On Mt. Dora Trail there is a 12-ft change in elevation for every 6 ft of horizontal distance (a 2 : 1 ratio). On Park Trail there is only a 2-ft change in elevation for every 6 ft of horizontal distance (a 1 : 3 ratio). Finding Slope in an Application Determine the slope of the ramp up the stairs. Solution: Write the ratio for the slope and simplify. The slope is 12 . 8 16 1 2 Slope change in y change in x 8 ft 16 ft Example 1 Slope change in y change in x 12 ft 6 ft 2 1 Slope 2 2 ft 6 ft 1 3 (Change in x) 6 ft (Change in y) 2 ft Park Trail A B (Change in x) 6 ft A B (Change in y) 12 ft Mt. Dora Trail Skill Practice 1. Determine the slope of the aircraft’s takeoff path. Answer 1. 500 6000 6000 ft 1 12 16 ft 8 ft Slope change in y change in x rise run Figure 3-15 Change in y (rise) 500 ft Classroom Example: p. 244, Exercise 10
miller_introductory_algebra_3e_ch1_3
To see the actual publication please follow the link above