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Two-variable data: Models and scatterplots SAT question

Math · Problem-Solving and Data Analysis · Hard · Answer it here, explanation included.

The figure presents a scatterplot titled “Ice Cream Sales.” The horizontal axis is labeled “Temperature, in degrees Celsius,” and the integers 10 through 26, in increments of 2, are indicated. The vertical axis is labeled “Sales, in dollars,” and the integers 300 through 1,000, in increments of 100, are indicated. There are 12 data points in the scatterplot, and the line of best fit is drawn. The line of best fit begins slightly above the horizontal axis, and slightly to the right of the vertical axis, and slants upward and to the right. It passes through the point 12 comma 480 and the point 24 comma 880.

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?

ExplanationShow

Choice D is correct. On the line of best fit, d increases from approximately 480 to 880 between $t equals 12$ and $t equals 24$ . The slope of the line of best fit is the difference in d-values divided by the difference in t-values, which gives $the fraction with numerator 880 minus 480, and denominator 24 minus 12, end fraction, equals, the fraction 400 over 12$ , or approximately 33. Writing the equation of the line of best fit in slope-intercept form gives $d equals, 33 t plus b$ , where b is the y-coordinate of the y-intercept. This equation is satisfied by all points on the line, so $d equals 480$ when $t equals 12$ . Thus, $480 equals, 33 times 12, plus b$ , which is equivalent to $480 equals, 396 plus b$ . Subtracting 396 from both sides of this equation gives $b equals 84$ . Therefore, an equation for the line of best fit could be $d equals, 33 t plus 84$ .

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 $\text{[math]}$ rather than the value of d at $t equals 0$ . 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 $t equals 10$ rather than the value of d at $t equals 0$ . 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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Two-variable data: Models and scatterplots SAT question

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