Question 55·Easy·Two-Variable Data: Models and Scatterplots
A student recorded the number of hours they practiced free throws each week and the number of free throws they made out of 100 attempts. The results are shown in the scatterplot.
According to the trend shown by the data, what is closest to the predicted number of free throws the student would make (out of 100) after practicing for hours in a week?
For a prediction from a scatterplot, focus on the overall linear trend rather than any single point. Pick two points that lie on the trend and are easy to compare (especially 1 unit apart in ) to estimate the change in per 1 unit of , then move from a nearby plotted -value to the requested -value using that change.
Hints
Look at how the points change
Compare the y-values of two points that are 1 hour apart, such as the points above and on the x-axis.
Find the approximate increase per hour
Compute the change in the number made when practice time increases by hour.
Extend the pattern one more hour
Use the point near hours and adjust it by the per-hour change to estimate the value at hours.
Desmos Guide
Plot the points
Enter the points from the scatterplot, for example:
Draw a line matching the trend
Create a line through two points on the trend, such as and . The slope is , so enter a line like and adjust until the line goes through the plotted points (it should fit them closely).
Read the prediction at
Use the line you entered and evaluate it at (you can make a table for the line with ). The y-value you get is the predicted number of free throws made.
Step-by-step Explanation
Estimate the rate of change
Use two nearby points on the trend, such as and . When practice time increases by hour, the number made increases by .
Predict at 9 hours
From hours to hours is one more hour, so add about to the value near .
So the predicted number of free throws made is 89.