Question 1·Easy·Two-Variable Data: Models and Scatterplots
A scatterplot shows the relationship between the distance from a Wi-Fi router, (in meters), and the download speed, (in megabits per second), for several locations in a building. A line of best fit for the data is given by
Which choice best describes what the number 72 represents in this model?
When a line of best fit is written as , interpret as the predicted value of when and interpret as the predicted change in for a 1-unit increase in . Then select the choice that matches the requested parameter.
Hints
Use slope-intercept form
The model is written in the form . Think about what and represent.
Focus on the constant term
The number 72 is the term that does not multiply . What does that tell you about the value of when ?
Plug in
Evaluate when to interpret the model at the router.
Desmos Guide
Graph the model
Enter in Desmos.
Check the intercept
Find the point where the line crosses the -axis (this occurs at ). Read the corresponding -value.
Match to the statement
Choose the option that describes the predicted download speed when the distance from the router is 0 meters.
Step-by-step Explanation
Identify the intercept
In the form , the constant term is the -intercept. Here, .
Interpret the intercept in context
The -intercept is the predicted value of when . So when the distance from the router is 0 meters, the predicted download speed is 72 megabits per second.