A line of best fit gives predictions from the overall pattern of a scatterplot. If the question gives the output and asks for the input, use two clear points on the drawn line to find its slope, then solve for the input in Desmos. Measured dots aren't the prediction, and an axis labeled in thousands needs a final unit conversion.
Hints
- Hint 1
A line of best fit follows the overall trend; filled dots show individual days. The hollow markers lie on the line, so which two coordinates should you use to describe the prediction rule?
- Hint 2
The slope is the change in calories divided by the change in steps. Use the two marked points, and remember that the horizontal values are in thousands of steps, not single steps.
- Hint 3
To find an input from an output, set the line's predicted calories equal to the requested calorie amount. After you solve for the horizontal value, what conversion does the axis label require?
Step-by-step
Use the marked line points and solve
Step 1Choose points on the prediction line
The hollow markers and are on the line of best fit. Use them rather than the filled dots, which are observations: calories burned on individual days. The horizontal coordinates are in thousands of steps.
- Step 2
Find the line's slope
The slope is the change in calories divided by the change in horizontal value. Type in Desmos. It shows , so the line predicts 20 more calories per thousand steps.
- Step 3
Translate the calorie target into an equation
Let be the number of steps in thousands. At , the line predicts calories; moving thousand-step units changes that prediction by . Set it equal to the target:
- Step 4
Solve for thousands of steps
Type in Desmos. The asks Desmos to solve for ; use instead of so it solves rather than graphs. Under PARAMETERS, it shows . That's 10.5 thousand steps, not 10.5 steps.
- Step 5
Convert to the requested number of steps
Type in Desmos to convert from thousands of steps. It shows , so the predicted value of is 10,500 steps when the person burns calories. Choice B.