Question 35·Medium·Two-Variable Data: Models and Scatterplots
A wildlife scientist records the number of weeks since a river-restoration project began, , and the number of fish observed during a standard survey, . A scatterplot of the data is shown, along with a line of best fit.
Two points on the line of best fit are labeled and . Which choice is the equation of the line of best fit?
When a best-fit line is shown and two points on it are labeled, treat it like an exact line problem: compute the slope from the two points, then substitute one point into to find the intercept. Finally, pick the option that matches both and .
Hints
Use the labeled points on the line
The equation of the line of best fit can be found from the two labeled points and .
Compute the slope
Find using .
Find the intercept
After you know , plug one labeled point into and solve for .
Desmos Guide
Plot the two labeled points
In Desmos, enter the points and .
Create the line through the points
Use the Line tool (or enter y-18= m(x-2) after computing ) to represent the line through the two points.
Write the equation in slope-intercept form
Find the slope between the two points and then compute using for one point. This gives the equation .
Step-by-step Explanation
Find the slope from the two labeled points
Use the two labeled points and :
Use to find the intercept
Substitute into :
So , which means .
Select the matching equation
With slope and intercept , the line of best fit is .
Therefore, the correct choice is .