6.6 Graphing Linear Equations 347 axis with the dependent variable and the horizontal axis with the independent variable. For the equation C n3 5, = + the C is the dependent variable and the n is the independent variable. Thus, to graph this equation, we label the vertical axis C and the horizontal axis n. In many graphs, the values to be plotted on one axis are much greater than the values to be plotted on the other axis. When that occurs, we can use different scales on the horizontal and the vertical axes, as illustrated in Examples 10 and 11. The next two examples illustrate applications of graphing. d t 80 160 240 d 5 40t 6 4 Time (hr) Distance (miles) 2 0 Figure 6.20 230 260 290 P S 30 60 90 120 150 180 210 Break-even point 2000 3000 4000 5000 Sales (units) Profit ($1000s) 1000 Figure 6.21 Example 10 Using a Graph to Determine Distance The distance in miles, d, a car travels in t hours, traveling at a constant rate of 40 miles per hour, can be determined by the equation d t 40 . = a) Graph d t 40 , = for t 6. ≤ b) Use the graph to estimate the distance the car travels in 4 hours. Solution a) Since d t 40 = is a linear equation, the graph will be a straight line. Select three values for t, determine the corresponding values for d, and then draw the graph (Fig. 6.20). d t 40 = Let t 0, = d 40(0) 0 = = Let t 2, = d 40(2) 80 = = Let t 6, = d 40(6) 240 = = Now try Exercise 99 t d 0 0 2 80 6 240 b) By drawing a vertical line from t 4 = on the time axis up to the graph and then drawing a horizontal line across to the distance axis, we can estimate that the distance the car travels in 4 hours is about 160 miles. 7 Example 11 Using a Graph to Determine Profits Javier owns a business that sells mountain bicycles. He believes the profit (or loss) from the bicycles sold can be estimated by the formula P S 60 90,000, = − where S is the number of bicycles sold. a) Graph P S 60 90,000, = − for S 5000 ≤ bicycles. b) From the graph, estimate the number of bicycles that must be sold for the business to break even. c) From the graph, estimate the number of bicycles sold if the profit from selling bicycles is about $150,000. Solution a) Select values for S and determine the corresponding values of P. The graph is illustrated in Fig. 6.21. S P 0 90,000 − 2000 30,000 5000 210,000 Ollyy/Shutterstock Instructor Resources for Section 6.6 in MyLab Math • Objective-Level Videos 6.6 • Animation: Exploring Slope and y-intercept • PowerPoint Lecture Slides 6.6 • MyLab Exercises and Assignments 6.6
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