Question 11·Medium·Two-Variable Data: Models and Scatterplots
The scatterplot shows the relationship between the number of thousands of miles driven, , and the remaining thickness of a set of brake pads, , in millimeters. A line of best fit is also shown.
Two points on the line of best fit are labeled and .
Which equation best represents the line of best fit?
When a line of best fit is drawn, pick two easy-to-read points on the line (often labeled or at grid intersections). Compute the slope using , then write by reading the intercept at or substituting one point to solve for .
Hints
Use the labeled points
Choose two clear points that lie on the line of best fit. The graph labels two such points, and .
Find the slope
Compute the slope with using the coordinates of and .
Find the intercept
If one point has , its -value is the intercept in .
Desmos Guide
Compute the slope from the two points
In Desmos, compute m=(4-12)/(40-0).
Use y = mx + b
Since point is , set b=12 and enter y=m x + b.
Match the equation to the choices
Compare the equation you entered with the answer choices and select the matching one.
Step-by-step Explanation
Read two points on the line
From the graph, the labeled points on the line of best fit are and . (Here is in thousands of miles and is in millimeters.)
Compute the slope
Write the equation
Since point is at , the line’s -intercept is . Therefore the line of best fit is