Section 3.3 Slope of a Line and Rate of Change 243 This gives us the ordered pair (2000, 28300). In the year 2008, the income was $35,300. This gives the ordered pair (2008, 35300). Label the points. Apply the slope formula. Simplify. 12000, 283002 and 12008, 353002 1x1, y12 1x2, y22 35,300 28,300 2008 2000 7000 8 875 m y2 y1 x2 x1 The slope is 875. This tells us the rate of change of the y value (income) compared to the x value (years). This means that men’s median income in the United States increased at a rate of $875 per year during this time period. Section 3.3 Practice Exercises Study Skills Exercise Each day after finishing your homework, choose two or three odd-numbered problems or examples from that section. Write the problem with the directions on one side of a card. On the back write the section, page, and problem number along with the answer. Each week, shuffle your cards and pull out a few at random, to give yourself a review for -hr or more. Vocabulary and Key Concepts 1. a. The ratio of the vertical change and the horizontal change between two distinct points (x1, y1) and (x2, y2) For additional exercises, see Classroom Activities 3.3A–3.3C in the Student’s Resource Manual at www.mhhe.com/moh. 12 3 5 slope y2y1 on a line is called the of the line. The slope can be computed from the formula m . parallel b. Lines in the same plane that do not intersect are called lines. c. Two lines are perpendicular if they intersect at a right angle. d. If m1 and m2 represent the slopes of two nonvertical perpendicular lines then m1 m2 . e. The slope of a vertical line is . The slope of a line is 0. Review Exercises For Exercises 2–6, find the x- and y-intercepts (if they exist). Then graph the line. 2. 3. 4. y 2 3x 5 2 x 3y 6 x 1 2 3 4 5 5 4 y 1 21 2 3 4 5 6 7 8 x 3 2 1 x 5 2 1 2 3 4 5 5 4 y 1 2 1 2 3 4 5 6 7 8 x 3 2 1 x 3y 6 5 4 y 1 543 1 2 3 4 5 21 2 3 4 5 x 3 2 1 y x 2 3 x-intercept: (7, 0); y-intercept: none x-intercept: (6, 0); y-intercept: (0, 2) x-intercept: (0, 0); y-intercept: (0, 0) Writing Translating Expression Geometry Scientific Calculator Video x2x1 undefined horizontal 1
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