We said that the slope of a line is the ratio of the vertical change (rise) to the horizontal change (run). Therefore, Formula The Slope of a Line The slope (m) of a line containing the points (x1, y1) and (x2, y2) is given by m vertical change horizontal change y2 y1 x2 x1 We can also think of slope as: rise run or change in y change in x Let’s look at some different ways to determine the slope of a line. x y Run Rise Notice that the slope of a line is a ratio! It is the ratio of (y2 y1) to (x2 x1) or rise to run. EXAMPLE 2 Determine the slope of each line. a) x y B A 2 b) x y A 1 2 B 1 Solution a) We will fi nd the slope in two ways. i) First, we will fi nd the vertical change and the horizontal change by counting these changes as we go from A to B. y 2 t B Vertical change (change in y) from A to B: t 3 units A 2 Horizontal change (change in x) from A to B: 2 units x Slope change in y change in x 3 2 or m 3 2 ii) We can also fi nd the slope using the formula. Let (x1, y1) (2, 3) and (x2, y2) (4, 6). m y2 y1 x2 x1 6 3 4 2 3 2 You can see that we get the same result either way we fi nd the slope. 158 CHAPTER 4 Linear Equations in Two Variables and Functions www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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