Question 8·Medium·Two-Variable Data: Models and Scatterplots
The scatterplot shows the relationship between the number of practice sessions a student completes () and the student’s average time, in minutes, to solve a puzzle (). A line of best fit is shown.
Which choice best interprets the slope of the line of best fit?
When a line of best fit is shown, treat it like any line: pick two easy-to-read points on the line, compute , then interpret it with units. The sign matters: a downward line means the predicted decreases as increases.
Hints
Use the line, not the dots
To interpret slope, pick two convenient points on the line of best fit (not necessarily two data points).
Compute rise over run
Find using your two points on the line.
Attach meaning and units
Slope tells how many minutes changes for each 1-session increase in , and the sign tells whether it increases or decreases.
Desmos Guide
Enter two points from the line
In Desmos, type the two points the line passes through, for example:
(0,30)
(12,12)
Calculate the slope
In a new expression, compute the slope with rise over run:
(12-30)/(12-0)
Desmos will display the slope value.
Match the meaning to a choice
Use the sign (positive or negative) and the units (minutes per session) to choose the statement that correctly describes how predicted time changes for each additional practice session.
Step-by-step Explanation
Choose two points on the line
Use two clear points the line passes through, such as and .
Compute the slope
Interpret the slope in context
The slope is negative, so the predicted average time goes down as the number of practice sessions increases. The best interpretation is:
For each additional practice session, the predicted average time to solve a puzzle decreases by about 1.5 minutes.