Question 53·Medium·Two-Variable Data: Models and Scatterplots
A scatterplot shows the relationship between a car’s speed , in miles per hour (mph), and the braking distance , in feet, on a dry road. A line of best fit is drawn on the scatterplot.
Which choice is an equation of the line of best fit shown?
When a line of best fit is drawn, pick two grid-intersection points on the line to avoid estimation error. Compute the slope from those points, then substitute one point into to find , and match the resulting equation to the choices.
Hints
Use points on the line, not the scattered dots
For the equation of the line of best fit, pick two grid-intersection points the drawn line passes through.
Compute the slope
Use with your two chosen points.
Find the y-intercept
After you know , plug one point into to solve for .
Desmos Guide
Plot two points from the line
In Desmos, enter the two points the line passes through:
A=(20,50)B=(50,140)
Create the line through the points
Enter the line through and :
y-50=((140-50)/(50-20))(x-20)
Match to an answer choice
Simplify the line’s equation (or compare its slope and intercept) to identify which listed equation matches the Desmos line.
Step-by-step Explanation
Choose two points on the drawn line
From the graph, the line of best fit passes through the grid intersection points and .
Find the slope and intercept
Compute the slope:
Use to find in :
Write the equation
With and , the line’s equation is .