238 Chapter 3 Graphing Linear Equations in Two Variables y2 y1 x2 x1 1x1, y12 m x2 x1 0 y2 y1. x2 x1 (x2, y2) Finding the Slope of a Line Given Two Points 1x2, y22. Find the slope of the line through the points and . Solution: To use the slope formula, first label the coordinates of each point and then substitute the coordinates into the slope formula. Label the points. Apply the slope formula. Simplify to lowest terms. 11, 32 and 14, 22 1x1, y12 1x2, y22 The slope of the line can be verified from the graph (Figure 3-19). 5 4 y 1 5 4 3 1 2 3 4 5 1 2 3 4 5 2 1 Figure 3-19 x 3 2 ( 1, 3) ( 4, 2) 25 units 23 units 5 3 5 3 m y2 y1 x2 x1 122 132 142 112 11, 32 14, 22 Example 2 Skill Practice Find the slope of the line through the given points. 2. 15, 22 and 11, 32 Answer 2. 1 6 Slope Formula The slope of a line passing through the distinct points and is provided . Note: If x2 x1 0, the slope is undefined. 1x1, y12 1x2, y22 2. Slope Formula The slope of a line may be found using any two points on the line—call these points and 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: (Figure 3-18). The slope of a line is often symbolized by the letter m and is given by the following formula. Figure 3-18 Change in y y2 y1 x2 x1 Change in x (x1, y1) Classroom Example: p. 246, Exercise 36 Avoiding Mistakes When calculating slope, always write the change in y in the numerator.
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