Question 25·Easy·Two-Variable Data: Models and Scatterplots
A scatterplot shows the relationship between the number of trail cameras deployed in a wildlife preserve, , and the number of deer sightings recorded in one week, . A line of best fit for the data is shown with equation .
Which choice best describes what the constant term represents in this context?
For a line of best fit written as , the constant term is the y-intercept. Quickly interpret it by substituting ; the result is the model’s predicted value of when the explanatory variable is 0.
Hints
Look for the term without a variable
In , which number is not multiplied by ?
Use
To interpret the constant term, evaluate the model when .
Translate into words
After you find when , describe what that means using the context of cameras and sightings.
Desmos Guide
Graph the line of best fit
In Desmos, enter .
Find the intercept
Use a table (or click the graph) to see the value of when .
Interpret the intercept
The value at is the predicted number of deer sightings when 0 cameras are deployed, which matches the correct choice.
Step-by-step Explanation
Identify the constant term
In , the constant term is . This is the y-intercept of the line of best fit.
Interpret the y-intercept in context
The y-intercept gives the predicted value of when .
So the model predicts deer sightings in a week when 0 cameras are deployed.
Therefore, the correct choice is: The predicted number of deer sightings in a week when 0 cameras are deployed is 3.