Bluebook SAT Test Two-Variable Data: Models and Scatterplots 9 — Questions and Answers
Question 1: A scatterplot shows data modeled by y = 3x² + 2. What is the predicted value of y when x = 4?
- 50 (Correct answer)
- 48
- 14
- 54
Correct answer: 50
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?
- y decreases by |m| (Correct answer)
- y increases by m
- y stays constant
- y decreases by b
Correct answer: y decreases by |m|
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?
- y = 3x + 1 (Correct answer)
- y = 4x
- y = 2x + 2
- y = 3x + 4
Correct answer: y = 3x + 1
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?
- For each additional hour of exercise per week, the resting heart rate decreases by 2.5 bpm on average. (Correct answer)
- The resting heart rate when exercise = 0 is −2.5 bpm.
- The maximum decrease in heart rate is 2.5 bpm.
- Exercise decreases heart rate by 2.5% per hour.
Correct answer: For each additional hour of exercise per week, the resting heart rate decreases by 2.5 bpm on average.
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?
- y = 2x + 5 (Correct answer)
- y = 2.5x + 5
- y = 2x − 5
- y = 5x + 2
Correct answer: y = 2x + 5
Slope = (25−5)/(10−0) = 20/10 = 2; y-intercept = 5 (given). Equation: y = 2x+5.
Question 6: A scatterplot of x and y has r = −0.88. Which of the following best describes the relationship?
- Strong negative linear relationship (Correct answer)
- Weak negative linear relationship
- Strong positive linear relationship
- No linear relationship
Correct answer: Strong negative linear relationship
r = −0.88 is close to −1, indicating a strong negative linear correlation.
Question 7: Data shows a pattern y ≈ 4 · 2^x. Which model best describes this data?
- Exponential (Correct answer)
- Linear
- Quadratic
- Constant
Correct answer: Exponential
The form y = a · b^x is an exponential model; here a = 4 and b = 2 (the growth factor).
Bluebook SAT Test Two-Variable Data: Models and Scatterplots 9
A scatterplot shows data modeled by y = 3x² + 2.
What is the predicted value of y when x = 4?