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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 “Minimum Wage.” The x axis is labeled “Years since 1940,” and the integers 0 through 80, in increments of 10, are indicated. The y axis is labeled “Minimum wage, in dollars per hour,” and the integers 0 through 8 are indicated. There are 8 data points in the scatterplot, and the line of best fit is drawn. The line of best fit begins at the point representing 0 years since 1940, minimum wage 0 dollars per hour. It slants upward and to the right, and passes through the point representing 40 years since 1940, minimum wage 3 point 3 5 2 dollars, and the point representing 70 years since 1940, minimum wage 6 point 2 3 2 dollars

The scatterplot above shows the federal-mandated minimum wage every 10 years between 1940 and 2010. A line of best fit is shown, and its equation is y equals, 0 point 0 9 6 x, minus 0 point 4 8 8. What does the line of best fit predict about the increase in the minimum wage over the 70-year period?

ExplanationShow

Choice A is correct. The given equation is in slope-intercept form, or y equals, m x plus b, where m is the value of the slope of the line of best fit. Therefore, the slope of the line of best fit is 0.096. From the definition of slope, it follows that an increase of 1 in the x-value corresponds to an increase of 0.096 in the y-value. Therefore, the line of best fit predicts that for each year between 1940 and 2010, the minimum wage will increase by 0.096 dollar per hour.

Choice B is incorrect and may result from using the y-coordinate of the y-intercept as the average increase, instead of the slope. Choice C is incorrect and may result from using the 10-year increments given on the x-axis to incorrectly interpret the slope of the line of best fit. Choice D is incorrect and may result from using the y-coordinate of the y-intercept as the average increase, instead of the slope, and from using the 10-year increments given on the x-axis to incorrectly interpret the slope of the line of best fit.

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