Question 52·Easy·Two-Variable Data: Models and Scatterplots
A scatterplot shows the relationship between the distance traveled, , in kilometers, by a delivery robot during a test run and the energy used, , in watt-hours.
A line of best fit for the data is given by .
Which choice best describes the meaning of the number in this context?
For questions about a line of best fit in the form , remember: (the coefficient of ) is the slope and represents the change in for a 1-unit increase in , while is the predicted value of when . Always include the context units when interpreting.
Hints
Look at the form of the equation
Compare to .
Focus on the coefficient of
The number multiplying tells how fast changes as increases.
Use the units of the axes
is in kilometers and is in watt-hours, so the slope’s units are “watt-hours per kilometer.”
Desmos Guide
Graph the line
In Desmos, enter .
Use two points to confirm the slope
Pick two points on the line, such as and , and compute the rise over run: .
Interpret the slope with units
The rise/run value represents how many watt-hours increases for each additional kilometer .
Step-by-step Explanation
Identify what the coefficient of represents
In the line of best fit , the coefficient of (which is 45) is the slope.
Slope means “how much changes when increases by 1.”
Attach the correct units and interpretation
Here, is kilometers and is watt-hours, so a slope of 45 means the energy used increases by about 45 watt-hours for each 1 additional kilometer traveled.
Therefore, the best description is: For each additional kilometer traveled, the robot uses about 45 more watt-hours of energy.