Question 29·Medium·Two-Variable Data: Models and Scatterplots
A scatterplot shows the relationship between the number of books a student read in a month and the student’s vocabulary test score. A line of best fit is shown on the graph.
Based on the line of best fit, which choice is the predicted vocabulary test score for a student who read 8 books in a month?
When a line of best fit is shown, use two clear points on the line to find the slope and then write . After you have the model, substitute the given -value to make the prediction; don’t use a nearby scatterplot point unless the question explicitly tells you to.
Hints
Use two clear points on the line
The line of best fit is drawn through and . Use these to find the slope.
Write the line equation
Compute the slope , then use . Since one point is at , you can read directly.
Evaluate at 8 books
Substitute into your equation to get the predicted test score.
Desmos Guide
Plot the two points on the line
Enter the points and in Desmos.
Create the line through the points
Type line(A,B) to graph the line through those two points.
Find the predicted value at
Type and click the intersection with the line, or type after determining the slope and intercept from the points.
Step-by-step Explanation
Find the slope from two points on the line
From the graph, the line of best fit passes through and . The slope is
Write an equation for the line of best fit
Because the line passes through , the -intercept is 62. Using , an equation for the line is
Predict when
Substitute :
The predicted vocabulary test score is 98.