148 Chapter 2 Linear Equations in Two Variables and Functions TIP: The slope formula does not depend on which point is labeled (x1, y1) and which point is labeled (x2, y2). For example, reversing the order in which the points are labeled in Example 2 results in the same slope: 11, 12 and 17, 22 then m 1x1, y11x2, y2 2 2 1 2 1 7 3 6 1 2 Finding the Slope of a Line Through Two Points Find the slope of the line passing through the points (3,4) and (5,1). Solution: Label points. Apply the slope formula. Simplify. 13, 42 and 15, 12 1x1, y1 1x2, y22 2 The two points can be graphed to verify that is the correct slope (Figure 2-16). Skill Practice Find the slope of the line passing through the given points. 3. (1, –8) and (–5, –4) 38 3 8 3 8 m y2 y1 x2 x1 1 142 5 3 Example 3 5 4 3 2 1 28 21 22 23 24 25 1 2 3 4 5 25242322 Figure 2-16 Positive slope Negative slope Zero slope Undefined slope y x (25, 21) 3 (3, 24) The line slopes m 5 238 downward from left to right. Skill Practice 2. Find the slope of the line that passes through the points (–4, 5) and (6, 8). Answers 2. 3. 2 3 3 10 When you apply the slope formula, you will see that the slope of a line may be positive, negative, zero, or undefined. • Lines that “increase,” or “rise,” from left to right have a positive slope. • Lines that “decrease,” or “fall,” from left to right have a negative slope. • Horizontal lines have a zero slope. • Vertical lines have an undefined slope.
miller_intermediate_algebra_4e_ch1_3
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