Section 2.2 Slope of a Line and Rate of Change 147 Answer 1. 2 5 Skill Practice 1. Find the slope of the roof. y y2 y1 x x2 x1 (x2, y2) (x1, y1) Change in y Change in x 8 ft 20 ft 2. The Slope Formula The slope of a line may be found by using any two points on the line—call these points (x1, y1) and (x2, y2).The change in y between the points can be found by taking the difference of the y-values: The change in x can be found by taking the difference of the x-values in the same order: The slope of a line is often symbolized by the letter m and is given by the Formula for the Slope of a Line Given Two Distinct Points The slope of a line passing through the distinct points (x1, y1) and (x2, y2) is m y2 y1 x2 x1 provided x2 x1 0 following formula. x2 x1. y2 y1. Finding the Slope of a Line Through Two Points Find the slope of the line passing through the points (1,1) and (7, 2). Solution: To use the slope formula, first label the coordinates of each point, and then substitute their values into the slope formula. Label the points. Apply the slope formula. Simplify. 11, 12 and 17, 22 1x1, y1 1x2, y22 2 1 2 3 6 m y2 y1 x2 x1 2 112 7 1 Example 2 5 4 3 2 1 2221 2 3 4 5 6 7 8 Figure 2-15 21 22 23 24 25 x y (7, 2) (1, 21) 6 3 The slope of the line can be verified from 1 the graph (Figure 2-15). Avoiding Mistakes When applying the slope formula, y2 and x2 are taken from the same ordered pair. Likewise y1 and x1 are taken from the same ordered pair.
miller_intermediate_algebra_4e_ch1_3
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