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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 “Total Protein and Total Fat for Eight Sandwiches.” The horizontal axis is labeled “Total protein,” in grams, and the numbers zero through 50, in increments of 10, are indicated. The vertical axis is labeled “Total fat,” in grams, and the numbers zero through 80, in increments of 10, are indicated. Eight data points and the line of best fit are shown. The line of best fit touches all 8 data points and extends upward and to the right through the following coordinates. All data are approximate.

Protein, 9 grams; Fat, 17 grams.
Protein, 20 grams; Fat, 33 grams.
Protein, 30 grams; Fat, 48 grams.
Protein, 40 grams; Fat, 63 grams.
Protein, 48 grams; Fat, 75 grams.

The scatterplot above shows the numbers of grams of both total protein and total fat for eight sandwiches on a restaurant menu. The line of best fit for the data is also shown. According to the line of best fit, which of the following is closest to the predicted increase in total fat, in grams, for every increase of 1 gram in total protein?

ExplanationShow

Choice C is correct. The predicted increase in total fat, in grams, for every increase of 1 gram in total protein is represented by the slope of the line of best fit. Any two points on the line can be used to calculate the slope of the line as the change in total fat over the change in total protein. For instance, it can be estimated that the points $with coordinates 20 comma 34$ and $with coordinates 30 comma 48$ are on the line of best fit, and the slope of the line that passes through them is $the fraction with numerator 48 minus 34, and denominator 30 minus 20, end fraction, equals 14 over 10$ , or 1.4. Of the choices given, 1.5 is the closest to the slope of the line of best fit.

Choices A, B, and D are incorrect and may be the result of incorrectly finding ordered pairs that lie on the line of best fit or of incorrectly calculating the slope.

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Two-variable data: Models and scatterplots SAT question

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