Question 884·Medium·Math

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A scatterplot shows the relationship between the distance a cyclist rides in a week and the total calories the cyclist burns that week. Let $x$ be the number of 5-kilometer segments the cyclist rides in a week, and let $y$ be the total calories burned that week. A line of best fit for the data is given by

y = 275x + 160

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?

The phrase “for each additional” asks for a rate. In a line of best fit, the slope gives the predicted change in output for one unit of input. Check what one input unit represents before using that rate: it may cover several kilometers. The intercept gives a prediction at zero, not a change.

Hints

Hint 1
In a linear model $y=mx+b$ , the slope $m$ is the change in predicted $y$ when $x$ increases by $1$ . Which number in the given equation has that job?
Hint 2
A unit rate is a rate for one of the units requested. Here, one increase in $x$ means one 5-kilometer segment. How can you turn calories per segment into calories per kilometer?

Step-by-step

Interpret the slope, then convert its units
Step 1
Read the predicted change from the line
No Desmos needed. The equation gives the slope directly, and the unit conversion takes one division. The slope is the coefficient of $x$ , so $275$ means the line predicts 275 more calories when $x$ increases by $1$ . The $160$ is the prediction at $x=0$ , not an increase.
Step 2
Convert the rate to calories per kilometer
One increase in $x$ means 5 more kilometers, not 1. So divide the slope by $5$ to get the rate per kilometer:
$\frac{275\text{ calories}}{5\text{ kilometers}}=55\text{ calories per kilometer}.$
The line predicts approximately $55$ additional calories burned for each additional kilometer. Choice B.

Question 884·Medium·Math

Strategy

Hints

Step-by-step

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