Bluebook SAT Test Two-Variable Data: Models and Scatterplots 9

Question 1

A scatterplot shows data modeled by y = 3x² + 2. What is the predicted value of y when x = 4?

Accepted Answer

50

Answer

Substitute x=4: y = 3(16)+2 = 48+2 = 50.

Question 2

In a linear model y = mx + b, the slope m is negative. Which of the following is true as x increases by 1?

Accepted Answer

y decreases by |m|

Answer

A negative slope means each unit increase in x causes y to decrease by the magnitude of m.

Question 3

A scatterplot shows points (1, 4), (2, 7), (3, 10), (4, 13). Which equation fits this data exactly?

Accepted Answer

y = 3x + 1

Answer

Check slope: (7−4)/(2−1) = 3; y-intercept from (1,4): 4 = 3(1)+b → b=1. Equation: y=3x+1.

Question 4

The line of best fit for data on weekly exercise hours (x) and resting heart rate (y, bpm) is y = −2.5x + 80. What does the −2.5 represent?

Accepted Answer

For each additional hour of exercise per week, the resting heart rate decreases by 2.5 bpm on average.

Answer

The slope −2.5 represents the average change in y (resting heart rate) per unit increase in x (weekly exercise hours).

Question 5

A best-fit line passes through (0, 5) and (10, 25). What is the equation of this line?

Accepted Answer

y = 2x + 5

Answer

Slope = (25−5)/(10−0) = 20/10 = 2; y-intercept = 5 (given). Equation: y = 2x+5.

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