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messersmith_power_intermediate_algebra_1e_ch4_7_10

3 Use Slope to Solve Applied Problems EXAMPLE 3 EXAMPLE 4 The graph models the number of students at DeWitt High School from 2006 to 2012. a) How many students attended the school in 2006? in 2012? b) What does the sign of the slope of the line segment mean in the context of the problem? c) Find the slope of the line segment, and explain what it means in the context of the problem. Solution a) We can determine the number of students by reading the graph. In 2006, there were 1276 students, and in 2012 there were 1780 students. y Number of Students at DeWitt High School (2012, 1780) (2006, 1276) 2010 Year Number 1800 1700 1600 1500 1400 1300 1200 2012 2006 2008 b) The positive slope tells us that from 2006 to 2012 the number of students was increasing. c) Let (x1, y1) (2006, 1276) and (x2, y2) (2012, 1780). Slope y2 y1 x2 x1 1780 1276 2012 2006 504 6 84 x The slope of the line is 84. Therefore, the number of students attending DeWitt High School between 2006 and 2012 increased by 84 per year. Do all lines slant upward or downward? Let’s look at Example 4. 4 Find the Slope of Horizontal and Vertical Lines Find the slope of the line containing each pair of points. a) (1, 2) and (3, 2) b) (3, 4) and (3, 1) Solution a) Let (x1, y1) (1, 2) and (x2, y2) (3, 2). m y2 y1 x2 x1 2 2 3 (1) 0 4 0 If we plot the points, we see that they lie on a horizontal line. Each point on the line has a y-coordinate of 2, so y2 y1 always equals zero. The slope of every horizontal line is zero. Remember that if the numerator of a fraction is 0 and the denominator is nonzero, the fraction is equal to 0. Horizontal lines are neither going up or down, and therefore they have a slope of zero. x y 5 1 2 2 5 5 5 160 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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