Question 20·Medium·Two-Variable Data: Models and Scatterplots
The scatterplot shows the relationship between the number of practice sessions a student completes for a typing program and the student’s time to type a passage, where is the number of practice sessions and is the time (in seconds).
[The figure is provided.]
Which choice could be an equation of the line of best fit shown?
For an equation of a line of best fit, focus on two features you can read from the graph: the y-intercept (the predicted value when ) and the slope (the change in for a convenient change in ). Estimate two clear points on the drawn line, compute slope as rise over run, then choose the option with that slope and the matching intercept.
Hints
Estimate the intercept
Look at where the line of best fit crosses the -axis (when ).
Estimate the slope from two clear points
Pick two points the line passes near (for example, at and around ) and compute rise over run.
Check the sign
Decide whether the line slopes upward or downward as increases; that determines whether the slope should be positive or negative.
Desmos Guide
Plot two points from the drawn line
Enter the points and in a table (or as points) to match two locations on the line of best fit.
Compute the slope in Desmos
In an expression line, compute to see the slope of the line through those points.
Compare candidate equations visually
Graph each answer choice (one at a time) and see which line passes near and and matches the downward trend in the scatterplot.
Step-by-step Explanation
Read two points on the line of best fit
From the graph, the line of best fit passes through points close to and .
Find the slope
Compute the slope using the two points:
So the time decreases by about seconds per practice session.
Use the y-intercept to write the equation
When , the line is at about , so the y-intercept is . With slope , an equation matching the line is .