Darius is studying the relationship between mathematics and art. He asks friends to each draw a "typical” rectangle. He measures the length and width in centimeters of each rectangle and plots the points on a graph, where x represents the width and y represents the length. The points representing the rectangles are (6.1, 12.0), (5.0, 8.1), (9.1, 15.2), (6.5, 10.2), (7.4, 11.3), and (10.9, 17.5). Which equation could Darius use to determine the length, in centimeters, of a "typical” rectangle for a given width in centimeters?
Use a line of best fit for the data, with width as x and length as y. The mean width is 7.5 cm and the mean length is about 12.38 cm; the slope calculated from the points is about 1.518. The intercept is about 12.38 − 1.518(7.5) = 0.995, so the equation is y = 1.518x + 0.995, choice C.
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