Question 17·Medium·Two-Variable Data: Models and Scatterplots
The scatterplot shows the relationship between the flow rate of water through a device, , and the rotation speed of a turbine, , along with a line of best fit.
According to the line of best fit, a flow rate of approximately how many liters per minute is predicted to produce a rotation speed of revolutions per minute?
When a question asks for an -value that gives a particular predicted -value, use the line of best fit as the equation , substitute the given predicted value for , and solve the resulting linear equation for .
Hints
Find the model equation
Read the equation of the line of best fit shown on the scatterplot.
Plug in the predicted speed
Because the question says “predicted,” use and set it equal to .
Solve for
Isolate using inverse operations (subtract the intercept, then divide by the slope).
Desmos Guide
Enter the best-fit line
In Desmos, type .
Add the target speed as a horizontal line
Type .
Find the intersection’s -value
Click the intersection point of the two lines and read its -coordinate.
State the result
The intersection occurs at , so the predicted flow rate is liters per minute.
Step-by-step Explanation
Use the line of best fit as a model
From the graph, the line of best fit is labeled , where is flow rate (liters per minute) and is the predicted rotation speed (revolutions per minute).
Set the predicted value equal to 250
Set to :
Subtract from both sides:
Solve for and select the matching choice
Divide both sides by :
The predicted flow rate is liters per minute, so the correct choice is .