EXAMPLE 1 A sign along a highway through the Rocky Mountains is shown on the left. What does this mean? Solution Percent means “out of 100.” Therefore, we can write 7% as as the ratio of the vertical change in the road to horizontal change in the road. The slope of the road is 7 100 . dd vertical change horizontal change The highway rises 7 ft for every 100 horizontal feet. YOU TRY 1 The slope of a skateboard ramp is 7 16 where the dimensions of the ramp are in inches. What does this mean? 2 Find the Slope of a Line Given Two Points on the Line Here is line L. The points (x1, y1) and (x2, y2) are two points on line L. We will fi nd the ratio of the vertical change in y to the horizontal change in x between the points (x1, y1) and (x2, y2). To get from (x1, y1) to (x2, y2), we move vertically to point P then horizontally to (x2, y2). The x-coordinate of point P is x1 and the y-coordinate of P is y2. When we moved vertically from (x1, y1) to point P(x1, y2), how far did we go? We moved a vertical distance y2 y1. 5 P x1 y2 t x2 y2 y2 y1 t 5 5 Note The vertical change is y2 y1 and is called the rise. 7 100 Then we moved horizontally from point P(x1, y2) to (x2, y2). How far did we go? We moved a horizontal distance x2 x1. Note The horizontal change is x2 x1 and is called the run. . We can interpret 7 100 t x2 x1 x y x1 y1 5 t www.mhhe.com/messersmith SECTION 4.2 Slope of a Line and Slope-Intercept Form 157
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