Question 47·Medium·Two-Variable Data: Models and Scatterplots
The scatterplot shows the relationship between the number of workouts per week for a group of adults and their resting heart rate, where is the number of workouts per week and is resting heart rate (in beats per minute). A line of best fit is shown on the scatterplot.
[The figure is provided.]
Which choice could be an equation of the line of best fit shown?
For a line-of-best-fit equation, estimate the -intercept by finding where the drawn line crosses the vertical axis, then estimate the slope using two easy-to-read points on the line (often near the ends of the graph). Finally, choose the option with both the correct intercept and the correct slope sign and size.
Hints
Look at where the line crosses the vertical axis
Estimate the value of when by reading where the line meets the -axis.
Use two clear points on the drawn line
Pick two points on the line (such as near the left edge and right edge) and compute slope as change in divided by change in .
Check the sign of the slope
Decide whether the line goes up or down as increases, and make sure the equation’s slope has the same sign.
Desmos Guide
Graph the answer choices as lines
Enter the four equations (one per line) in Desmos:
Compare to two points from the drawn line
From the figure, the drawn line goes near and . In Desmos, check which graphed equation passes near both of those points.
Use a quick visual check for steepness and direction
Eliminate any line that slopes upward, and eliminate any line that drops much faster than the line in the figure. The remaining line matches the one shown.
Step-by-step Explanation
Estimate the -intercept
From the graph, the line of best fit crosses the vertical axis at about when . So the equation should start with .
Estimate the slope from two points on the line
Two convenient points on the drawn line are approximately and .
The slope is
Match the equation to intercept and slope
An intercept of and slope of gives .
Therefore, the correct choice is .