146 Chapter 2 Linear Equations in Two Variables and Functions To measure the slope of a line quantitatively, consider two points on the line. The slope is the ratio of the vertical change between the two points to the horizontal change. That is, the slope is the ratio of the change in y to the change in x. As a memory device, we might think of the slope of a line as “rise over run.” change in y change in x To move from point A to point B on the stairs, rise 3 ft and move to the right 4 ft (Figure 2-13). 4-ft change in x rise run B Figure 2-13 3-ft change in y Change in x (run) Slope change in y change in x Change in y (rise) 3 ft 4 ft 3 4 Slope To move from point A to point B on the wheelchair ramp, rise 3 ft and move to the right 18 ft (Figure 2-14). 18-ft change in x Figure 2-14 Slope change in y change in x 3 ft 18 ft 1 6 The slope of the stairs is , which is greater than the slope of the ramp, which is 16 . 34 Finding the Slope in an Application A A Example 1 Find the slope of the ladder against the wall. Solution: change in y change in x 15 ft 5 ft or 3 31 Slope 3 1 5 ft 15 ft 3-ft change in y B The slope is , which indicates that a person climbs 3 ft vertically for every 1 ft traveled horizontally.
miller_intermediate_algebra_4e_ch1_3
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