Question 33·Hard·Two-Variable Data: Models and Scatterplots
Each dot in the scatterplot represents the number of steps a person walked in one day and the number of calories the person burned from walking that day. A line of best fit is shown.
Let be the number of steps walked in a day. Based on the line of best fit, which choice is closest to the predicted value of when the person burns calories from walking?
When a scatterplot includes a line of best fit, treat the line like any other linear graph: pick two clear points on the line (here they are labeled), compute the slope, and write . Then be careful with axis units—if the x-axis is in thousands (or hundreds), solve in those units first and convert at the end.
Hints
Use the two labeled points on the line
The graph shows two points on the line of best fit with their coordinates. Use them to compute the slope.
Remember what the x-values represent
The x-axis is labeled in thousands of steps, not single steps. Keep track of that unit while you work.
Solve a linear equation
After you have an equation for the line, substitute for and solve for , then convert from thousands of steps to steps.
Desmos Guide
Enter the two labeled points on the line
Enter the points
A=(5,140)B=(11,260)
Create the line through those points
Compute the slope with an expression like
m=(260-140)/(11-5)
Then enter the line
y=m(x-5)+140
Find the x-value when y equals 250
Enter y=250 as another line. Click the intersection point of the two lines and note the x-coordinate (this x-value is in thousands of steps).
Convert to steps and match an answer choice
Multiply the x-coordinate you found by to convert from thousands of steps to steps, then select the matching option.
Step-by-step Explanation
Find the slope of the line of best fit
From the graph, the line of best fit passes through the labeled points and , where is measured in thousands of steps.
The slope is
So the model increases by about calories per additional 1 thousand steps.
Write an equation for the line
Use and the point :
So an equation for the line of best fit is , where is in thousands of steps.
Solve for the number of thousands of steps when
Set :
This means about thousand steps.
Convert to steps
Since represents thousand steps,
So the predicted number of steps is . Therefore, the correct choice is .