Section 2.4 Applications of Linear Equations and Modeling 175 a. Use the given ordered pairs to find a linear equation to model the number of women graduating from law school by year. b. Determine the slope of the line and interpret the meaning of the slope as a rate of change. c. Use the linear equation to predict the number of women who will graduate from law school in the year 2015. d. Would it be practical to use the linear model to predict the number of women who would graduate from law school for the year 2050? Solution: a. The slope formula can be used to compute the slope of the line between the points. and (x1, y1) (x2, y2) Label the points. Apply the slope formula. Apply the point-slope formula. Use the point (15, 16.8) and m 0.29. Clear parentheses. Solve for y.The equation is in slope-intercept form. m y2 y1 x2 x1 19.7 16.8 25 15 y y1 m1x x12 y 16.8 0.291x 152 y 16.8 0.29x 4.35 y 0.29x 12.45 b. The slope is 0.29.This means that the number of women who graduate from law school increased at a rate of 0.29 thousand (290) per year during this time period. c. The year 2015 is 35 years after the year 1980.Therefore, substitute x 35. y 0.291352 12.45 22.6 In the year 2015, we predict that approximately 22,600 women will graduate from law school. d. It would not be practical to use this equation to predict the number of women who will graduate from law school in the year 2050. It is unreasonable to assume that the linear trend will continue this far beyond the observed data. Skill Practice The figure shows data relating the cost of college textbooks (in dollars) to the number of pages in the book. Let y represent the cost of the book, and let x represent the number of pages. 7. Use the ordered pairs indicated in the figure to write a linear equation to model the cost of textbooks (in dollars) versus the number of pages. 8. What is the slope of this line and what does it mean in the context of this problem? 9. Use the equation to predict the cost of a textbook that has 360 pages. 2.9 10 0.29 115, 16.82 125, 19.72 Answers 7. y 0.25x 7 8. m 0.25; The cost of the textbook goes up by $0.25 per page. 9. $97 Cost ($) Cost of Textbook Versus Number 0 100 200 300 400 500 Number of Pages 120 100 80 60 40 20 0 of Pages (200, 57) (400, 107) y x
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