SAT Math · Two-variable data: models and scatterplots · easy

A line of best fit for a data set is given by y = 2.5x + 30, where x represents years of experience and y represents predicted salary in…

A line of best fit for a data set is given by y=2.5x+30y = 2.5x + 30, where xx represents years of experience and yy represents predicted salary in thousands of dollars. According to this model, what is the predicted salary, in thousands of dollars, for someone with 12 years of experience?

Answer and explanation

Answer: 60

Substitute 12 years of experience into the model: y=2.5(12)+30=30+30=60y = 2.5(12) + 30 = 30 + 30 = 60. The predicted salary is 60 thousand dollars, so the answer is 60. The slope of 2.5 means each additional year adds $2,500 to the predicted salary, and the intercept 30 is the predicted starting salary in thousands of dollars. A common wrong answer is 30, which forgets to multiply by 12 for the slope term. Another is 32.5, from adding 2.5+302.5 + 30 as if x=1x = 1. A third is 360, from multiplying 30×1230 \times 12. Plug in the value, multiply first, then add.

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