SAT Math: Scatterplots and Lines of Best Fit (Drill 1)

Question 1. A researcher measures the height, in centimeters, of a plant each week after planting a seed. The line of best fit for the data is y = 2.4x + 1.2, where x is the number of weeks after planting and y is the height in centimeters. What does the line of best fit predict about the plant's growth?

• A) The plant grows an average of 1.2 centimeters per week.
• B) The plant grows an average of 2.4 centimeters per week. ✓
• C) The plant was 2.4 centimeters tall when planted.
• D) The plant reaches a maximum height of 2.4 centimeters.

Explanation: In the equation y = 2.4x + 1.2, the slope is 2.4. The slope represents the average change in y for each one-unit increase in x. Since x is measured in weeks and y in centimeters, the slope means the plant grows an average of 2.4 centimeters per week. Choice A incorrectly uses the y-intercept (1.2) as the growth rate. Choice C confuses the slope with the initial height.

Question 2. Which of the following is closest to the slope of this line of best fit?

• A) 2
• B) −2 ✓
• C) 0.5
• D) −0.5

Explanation: The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is calculated as (y₂ − y₁) / (x₂ − x₁). Using the points (2, 17) and (10, 1): slope = (1 − 17) / (10 − 2) = −16/8 = −2. The line has a negative slope because y decreases as x increases. Choices A and C are incorrect because the slope is negative, not positive.

Question 3. What is the difference between the actual height at week 3 and the height predicted by the line of best fit at week 3?

• A) 0.2
• B) 1 ✓
• C) 1.4
• D) 11

Explanation: The actual height at week 3 is 11 cm (from the table). The predicted height from the line of best fit is y = 2.8(3) + 1.6 = 8.4 + 1.6 = 10.0 cm. The difference is 11 − 10.0 = 1.0. Choice A is too small. Choice C may result from a calculation error. Choice D is the actual y-value itself, not the difference.

Question 4. A city records the number of registered electric vehicles, in thousands, each year since 2015. The line of best fit is y = 3.8x + 2.1, where x is the number of years since 2015 and y is the number of electric vehicles in thousands. What does the number 2.1 represent in this equation?

• A) The predicted number of electric vehicles, in thousands, in 2015 ✓
• B) The predicted annual increase in electric vehicles, in thousands
• C) The total number of electric vehicles predicted by 2025
• D) The year when electric vehicle registration began

Explanation: In the equation y = 3.8x + 2.1, the value 2.1 is the y-intercept, the predicted value of y when x = 0. Since x represents years since 2015, x = 0 corresponds to 2015. Therefore, 2.1 represents the predicted number of electric vehicles, in thousands, in 2015. Choice B describes the slope (3.8), not the y-intercept.

Question 5. What is the average rate of change, in degrees Celsius per minute, of the water temperature from 2 minutes to 6 minutes?

• A) 4.5
• B) 6.25 ✓
• C) 12.5
• D) 25

Explanation: The average rate of change is the difference in y-values divided by the difference in x-values. At x = 2, the temperature is 34°C. At x = 6, the temperature is 59°C. Average rate of change = (59 − 34)/(6 − 2) = 25/4 = 6.25°C per minute. Choice C (12.5) may result from dividing by 2 instead of 4. Choice D (25) is just the numerator without dividing.