Question 40·Easy·Two-Variable Data: Models and Scatterplots
A scatterplot shows the relationship between , the number of weeks an athlete trained, and , the time (in seconds) it took the athlete to run 400 meters. A line of best fit is drawn on the scatterplot and has the equation .
Which choice best describes what the value represents in this context?
For line-of-best-fit interpretation questions, rewrite the equation mentally as . The slope is the “per 1 unit of ” change in the predicted , and the sign tells whether it increases (positive) or decreases (negative).
Hints
Find the slope
Look at the coefficient of in the equation of the line of best fit.
Translate the sign
Because the coefficient is negative, think about whether the predicted time goes up or down as weeks of training increase.
Use “per 1 unit” language
The coefficient of tells the change in predicted for each increase of 1 in .
Desmos Guide
Enter the line of best fit
Type .
Read what the slope means
Notice the number multiplying is . That number tells how much changes when increases by 1.
Confirm with a table
Click the table icon for the expression and compare two rows where differs by 1 (for example, and ). The -values differ by , showing the predicted time drops by 1.5 seconds per week.
Step-by-step Explanation
Identify the slope
In , the coefficient of is . This is the slope.
Interpret the slope in context
A slope of means that for each increase of 1 week in training, the predicted time decreases by 1.5 seconds.
Therefore, the correct choice is For each additional week of training, the predicted 400-meter time decreases by 1.5 seconds.