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Example 1 Suppose an airplane descends at a rate of 300 ft/min from an elevation of 8000 ft. Write and graph an equation to model the plane’s elevation as a function of the time it has been descending. Interpret the intercept at which the graph intersects the vertical axis An equation that models the plane’s elevation is d = –300t + 8000. An equation that models the plane’s elevation is d = –300t + 8000. The d-intercept is (0, 8000) which means the plane was at 8000 ft at the moment it began its descent. Example 2 A spring has a length of 8 cm when a 20-g mass is hanging at the bottom end. Each additional gram stretches the spring another 0.15 cm. Write an equation for the length y of the spring as a function of the mass x of the attached weight. Graph the equation. Interpret the y-intercept. Step 1: Identify the two points Reminder: mass is defined as x and length as y (x1, y1) would be the initial information (20, 8) Adding another 20 g of mass at the end of the spring will give a total mass of 40 g and a length of 8 + 0.15(20) = 11 cm. Use the points (x1, y1) = (20, 8) and (x2, y2) = (40, 11) to find the linear equation. Step 3: Use one of the points and the point-slope form to write an equation for the line. The y-intercept is (0, 5). So, when no weight is attached to the spring, the length of the spring is 5 cm.