Question 23·Medium·Two-Variable Data: Models and Scatterplots
The scatterplot shows the relationship between the number of minutes a delivery truck spends idling, , and the number of gallons of fuel used while idling, . A line of best fit is shown on the scatterplot.
According to the line of best fit, approximately how many gallons of fuel are used for each additional minute of idling?
When a scatterplot includes a line of best fit and asks for a rate like “per 1 unit of ,” you are being asked for the slope. Read two clear points from the line (prefer labeled or grid-intersection points), compute , and then match that value to the choice that has the correct magnitude and units.
Hints
Use the line of best fit
Pick two points that lie on the drawn line (labeled points are easiest to use).
Find the rate of change
Compute the slope using with your two points.
Match units to the question
Because is in gallons and is in minutes, the slope is in gallons per minute.
Desmos Guide
Enter two points from the line
In Desmos, create a table and enter the two labeled points and .
Compute the slope
In an expression line, type to compute the slope.
Interpret the value
The result is gallons per minute, since you divided a change in gallons by a change in minutes.
Step-by-step Explanation
Choose two points on the line of best fit
From the graph, the line of best fit passes through the labeled points and .
Set up the slope as a rate of change
Compute the slope (gallons per minute):
Interpret the slope in context
Now simplify the rate:
So, the truck uses about gallons of fuel for each additional minute of idling.