A linear model is a line that follows the overall trend of a scatterplot. Read whether the dots rise or fall, then put their coordinates in a Desmos table and fit a line with regression, which finds a line close to the dots. Compare its slope (change in per in ) and intercept (value at ) with the choices. The trap is treating one jump between dots as the slope of the whole trend.
Hints
- Hint 1
As you move right on a scatterplot, increases. If the dots rise too, the slope, or change in for each extra in , is positive. Which way do these dots go?
- Hint 2
Each dot gives one pair. Put all five pairs in a Desmos table, keeping each dot’s - and -coordinates in the same row. That lets the model use the whole pattern.
- Hint 3
Fit . A regression finds a line close to all the dots; Desmos reports and under PARAMETERS. Which equation has the closest slope and intercept?
Step-by-step
Fit the plotted points in Desmos
Step 1Read the direction of the trend
The dots rise from toward , so the slope, the change in for each increase in , is positive.
- Step 2
Enter the plotted pairs
Read each dot as an ordered pair and enter the five pairs in a Desmos table. Keep in one row. Swapping the columns would model from , not from .
- Step 3
Fit a line to the whole scatterplot
Type . The regression fits a line close to all five dots, rather than forcing it through one pair. Under PARAMETERS, Desmos reports for the slope and for the predicted -value when .
- Step 4
Match the fitted line to an equation
A best-fit line follows the trend; it needn’t hit every dot. Match both the slope and the intercept, not one dot. The closest coefficients to and are and , so the most appropriate model is . Choice D.