Problem-Solving and Data AnalysisHardLine of best fit interpretation
Problem-Solving and Data Analysis practice question
A scatterplot relates a plant's age in weeks (x) to its height in centimeters (y). The line of best fit is y = 2.5x + 4.
Which statement best interprets the slope of the line of best fit?
- A. The plant is 4 cm tall when first measured.
- B. The plant grows about 2.5 cm per week.Correct
- C. The plant grows about 4 cm per week.
- D. The plant is about 2.5 cm tall each week.
Answer: B. The plant grows about 2.5 cm per week.
In y = mx + b, the slope m = 2.5 is the change in y per one-unit change in x, i.e., 2.5 cm of height per additional week. The trap is confusing slope with the y-intercept 4 (the starting height, choice A/C).
Why the other answers are wrong
- A. The plant is 4 cm tall when first measured.
- That's a correct reading of the y-intercept 4 (height at week 0), but the question asks about the slope, which is the rate of growth.
- C. The plant grows about 4 cm per week.
- You picked the right idea — growth per week — but pulled the number from the y-intercept 4 instead of the slope 2.5.
- D. The plant is about 2.5 cm tall each week.
- You used the slope 2.5 but described it as a height rather than a rate; 2.5 is how much the height increases each week, not the height itself.
More Problem-Solving and Data Analysis questions
- Hard
The mean of five numbers is 12. If four of them are 8, 10, 14, and 16, what is the fifth number? - Hard
In a survey of 50 people, 30 like coffee, 20 like tea, and 8 like both. How many like neither? - Hard
A car travels at 60 mph for 2 hours, then 40 mph for 3 hours. What is its average speed for the whole trip? - Hard
Which statement correctly compares the standard deviations of the two sets? - Hard
How many milliliters of the 40% acid solution must the chemist add? - Hard
How many circuit boards were produced in the batch?
Not affiliated with the College Board. SAT is a trademark of the College Board.