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miller_intermediate_algebra_4e_ch1_3

Section 2.2 Slope of a Line and Rate of Change 149 Finding the Slope of a Line Through Two Points Example 4 Find the slope of the line passing through the points (3, 4) and (3,2). Solution: y 5 (3, 4) 3 2 1 2 3 4 Figure 2-17 x (3, 2) 1 2 3 4 5 1 54 321 5 Label points. Apply slope formula. Undefined 13, 42 and 13, 22 1x2, y21x1, y1 2 2 m y2 y1 x2 x1 6 3 3 6 0 2 4 3 132 The slope is undefined.The points form a vertical line (Figure 2-17). Skill Practice Find the slope of the line passing through the given points. 4. (5, –2) and (5, 5) Answers 4. Undefined 5. 0 Finding the Slope of a Line Through Two Points Example 5 Find the slope of the line passing through the points (0, 2) and (4, 2). Solution: Label the points. Apply the slope formula. Simplify. 10, 22 and 14, 22 1x2, y21x1, y1 2 2 m y2 y1 x2 x1 0 4 0 2 2 4 0 y 5 4 3 2 (4, 2) 1 2 3 4 The slope is zero.The line through the two points is a horizontal line (Figure 2-18). Skill Practice Find the slope of the line passing through the points. 5. (1, 6) and (–7, 6) 3. Parallel and Perpendicular Lines Lines in the same plane that do not intersect are parallel. Nonvertical parallel lines have the same slope and different y-intercepts (Figure 2-19). Lines that intersect at a right angle are perpendicular. If two lines are perpendicular, then the slope of one line is the opposite of the reciprocal of the slope of the other (provided neither line is vertical) (Figure 2-20). Figure 2-18 x 1 2 3 4 5 1 54 321 5 (0, 2)


miller_intermediate_algebra_4e_ch1_3
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