# Introduction to Abstract Algebra : Rings and Fields by Rachel Quinlan

By Rachel Quinlan

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Next, click the Show Legend box to remove the check mark. Click Finish at the bottom of the dialog box. The graph shown in Figure T4 will appear. y y = −(2/3)x + 2 −15 −10 FIGURE T4 The graph of y ϭ Ϫ23 x ϩ 2 over the interval 3Ϫ10, 104 −5 10 8 6 4 2 0 0 −2 −4 −6 5 10 15 x If the interval over which the straight line is to be plotted is not specified, then you may have to experiment to find an appropriate interval for the x-values in your graph. For example, you might first plot the straight line over the interval [Ϫ10, 10].

8 10. 30x Ϫ 20y ϭ 600 11. 1y Ϫ 352 ϭ 0 12. 3 Linear Functions and Mathematical Models Mathematical Models Regardless of the field from which a real-world problem is drawn, the problem is solved by analyzing it through a process called mathematical modeling. The four steps in this process, as illustrated in Figure 28, follow. 3 LINEAR FUNCTIONS AND MATHEMATICAL MODELS Real-world problem Formulate Solution of real-world problem Mathematical model Solve Test FIGURE 28 27 Interpret Solution of mathematical model Mathematical Modeling 1.

Plot the annual sales ( y) versus the year (x). b. Draw a straight line L through the points corresponding to 2000 and 2006. c. Derive an equation of the line L. d. Use the equation found in part (c) to estimate the annual sales of GPS equipment in 2005. Compare this figure with the projected sales for that year. Source: ABI Research 78. IDEAL HEIGHTS AND WEIGHTS FOR WOMEN The Venus Health Club for Women provides its members with the following table, which gives the average desirable weight (in pounds) for women of a given height (in inches): Height, x Weight, y 60 108 63 118 66 129 69 140 72 152 a.