Question 56·Medium·Two-Variable Data: Models and Scatterplots
A scatterplot shows the relationship between the distance a cyclist rides in a week and the total calories the cyclist burns that week. Let be the number of 5-kilometer segments the cyclist rides in a week, and let be the total calories burned that week. A line of best fit for the data is given by
According to the line of best fit, approximately how many calories are predicted to be burned for each additional kilometer the cyclist rides in a week?
When a linear model is given, the slope is always the rate of change in per 1 unit of . First identify what 1 unit of represents in the context (here, 5 kilometers), then convert the rate to the units the question asks for (here, per 1 kilometer) by multiplying or dividing as needed.
Hints
Focus on the slope
In a linear model , the slope tells how much changes when increases by 1 unit.
What does 1 unit of represent?
Here, is not kilometers. One unit of is one 5-kilometer segment.
Convert the rate
If the model changes by 275 calories per 5 kilometers, divide by 5 to get calories per 1 kilometer.
Desmos Guide
Enter the model
Type y=275x+160 into Desmos.
Compute the per-kilometer rate
In a new expression, type 275/5 to convert the slope from “per 5 kilometers” to “per 1 kilometer.”
Use the computed value
The value shown for 275/5 is the predicted calories burned per additional kilometer.
Step-by-step Explanation
Interpret the slope’s units
In , the slope means the model predicts an increase of calories for each increase of in .
Since counts 5-kilometer segments, an increase of in corresponds to an additional kilometers ridden.
Convert to calories per kilometer
Calories per kilometer:
So the model predicts about calories burned for each additional kilometer ridden.