Section 3.3 Slope of a Line and Rate of Change 239 1x1, y12 TIP: The slope formula is not dependent on which point is labeled and which point is labeled In Example 2, reversing the order in which the points are labeled results in the same slope. Label the points. 1x2, y22. 11, 32 and 14, 22 1x2, y22 1x1, y12 132 122 5 m 112 Apply the slope formula. 142 3 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 slope of zero. • Vertical lines have an undefined slope. Finding the Slope of a Line Given Two Points 32 2. 15, 12 Find the slope of the line passing through the points and Solution: a3 5, and b 2(x1, y1) (x2, y2) Label the points. Apply the slope formula. Simplify. 3 2b a1 2b 122 152 2, 15, 12 2 By graphing the points and we can verify that the slope is (Figure 3-20). Notice that the line slopes downward from left to right. 27 12, 32 2 7 or 2 7 4 2 2 5 m y2 y1 x2 x1 a a2, 1 2b 12, 2 Example 3 Skill Practice Find the slope of the line through the given points. 3. a2 3 , 0b and a Answer 3. 6 Positive Slope Negative Slope Zero Slope Undefined Slope 5 4 y 1 2221 252423 1 2 3 4 5 21 22 23 24 25 Figure 3-20 x 3 2 7 22 (2, 2 ) 32 (25, ) 12 1 6 , 5b Classroom Example: p. 246, Exercise 44 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_introductory_algebra_3e_ch1_3
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