Question 26·Medium·Two-Variable Data: Models and Scatterplots
A fitness coach recorded the time (in minutes) that each runner trained on a certain day and the runner’s resting heart rate (in beats per minute) the next morning. The scatterplot shows the data, and a line of best fit is drawn.
Which choice is the average rate of change, in beats per minute per minute of training, of the predicted resting heart rate from to according to the line of best fit?
When a question asks for an average rate of change from a line of best fit, treat it like finding a slope. Pick two clear points on the line at the given -values, compute , and keep track of the sign: a downward-trending line means a negative rate.
Hints
Use the line, not the scattered points
The question asks for the predicted change, so read values from the line of best fit.
Find the two y-values you need
Locate where the line of best fit is at and at , then note the corresponding -values.
Compute slope
Use with .
Desmos Guide
Enter two points from the line of best fit
In Desmos, create points and based on where the line of best fit crosses those -values.
Calculate the slope from the two points
Type
Desmos will display a value.
Match to a choice
Use the displayed value (it should be negative) and select the answer choice that matches it.
Step-by-step Explanation
Read two predicted values from the line
From the line of best fit on the graph, the predicted resting heart rate is beats per minute at and beats per minute at .
Compute the average rate of change
Average rate of change (slope) is
Simplify and select the matching choice
So the average rate of change is , and the correct choice is .