Question 872·Easy·Math

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A scatterplot shows the relationship between the distance traveled, $x$ , in kilometers, by a delivery robot during a test run and the energy used, $y$ , in watt-hours.

A line of best fit for the data is given by $y = 45x + 120$ .

Which choice best describes the meaning of the number $45$ in this context?

A line of best fit summarizes the trend of a scatterplot, so its slope describes a predicted change, not what happens at every dot. In $y=mx+b$ , the slope is $m$ : the output change for one more input unit. Use the axis labels to name that rate, and don’t confuse it with the starting value $b$ .

Hints

Hint 1
The slope of a line tells you how much its output changes when its input increases by $1$ . In $y=mx+b$ , which number multiplies $x$ , and what does its positive sign tell you?
Hint 2
A rate’s units combine the two axis labels: one quantity changes per unit of the other. Check which quantity is the input on the horizontal axis and which is the output on the vertical axis before stating the rate.

Step-by-step

Read the slope and its units
Step 1
Identify what 45 measures
No Desmos needed. Read the slope directly from the given line.

In $y=mx+b$ , the slope $m$ is the change in $y$ when $x$ increases by $1$ . Comparing the given equation with that form gives $m=45$ . The $120$ is the prediction at $x=0$ , so it’s not the rate of change.
Step 2
Say the rate in context
Here $x$ measures kilometers traveled and $y$ measures watt-hours used. Read slope as output change per input unit. So for each additional kilometer, the line predicts that the robot uses about $45$ more watt-hours of energy. Choice B.

Question 872·Easy·Math

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