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The scatterplot above shows a company’s ...


The scatterplot above shows a company’s ice cream sales d, in dollars, and the high temperature t, in degrees Celsius `(.^@C)`, on 12 different days. A line of best fit for the data is also shown. Which of the following could be an equation of the line of best fit?

A

d = 0.03t + 402

B

d = 10t + 402

C

d = 33t + 300

D

d = 33t + 84

Text Solution

Verified by Experts

The correct Answer is:
D
On the line of best fit, d increases from approximately 480 to 880 between t = 12 and t = 24. The slope of the line of best fit is the difference in d-values divided by the difference in t-values, which gives `(880-480)/(24-12)=400/12` , or approximately 33. Writing the equation of the line of best fit in slope-intercept form gives d = 33t + b, where b is the y-coordinate of the y-intercept. This equation is satisfied by all points on the line, so d = 480 when t = 12. Thus, 480 = 33(12) + b, which is equivalent to 480 = 396 + b. Subtracting 396 from both sides of this equation gives b = 84. Therefore, an equation for the line of best fit could be d = 33t + 84.
Choice A is incorrect and may result from an error in calculating the slope and misidentifying the y-coordinate of the y-intercept of the graph as the value of d at t = 10 rather than the value of d at t = 0. Choice B is incorrect and may result from using the smallest value of t on the graph as the slope and misidentifying the y-coordinate of the y-intercept of the graph as the value of d at t = 10 rather than the value of d at t = 0. Choice C is incorrect and may result from misidentifying the y-coordinate of the y-intercept as the smallest value of d on the graph.
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