The phrase “for each additional” signals a slope: the predicted change in score increase for one more practice test. With several recorded student pairs and a line of best fit, use a Desmos table and linear regression, then read the coefficient of the test count. A change between two students, or the line’s intercept, may look plausible but doesn’t describe the whole trend.
Hints
- Hint 1
The phrase “for each additional practice test” asks for a slope: how much the predicted score increase changes when the test count goes up by . You need a per-test rate, not a student’s total score increase.
- Hint 2
A line of best fit follows the overall trend; it needn’t pass through every row. Put test counts in Desmos’s column and score increases in , keeping each student’s two values together.
- Hint 3
For a linear regression, type . The tells Desmos to fit a line to the table. Read under PARAMETERS: it is the coefficient of the test count, which gives the per-test rate.
Step-by-step
Fit a line and read its slope
Step 1Identify the rate the question asks for
“Each additional practice test” asks for the slope, the change in predicted score increase when the test count goes up by . Write a line of best fit as , where means predicted score increase and is the rate in points per test.
- Step 2
Enter all eight student pairs
Create a Desmos table with test counts in and the matching score increases in . Desmos shows and as separate rows. Keep both: they are two observations, not one value to combine.
- Step 3
Fit the line and interpret its slope
Type below the table. The regression symbol tells Desmos to fit a line to all eight rows. Under PARAMETERS, it shows and . The slope gives the predicted score-increase points per additional test. The value predicts the increase at zero tests; it is not the per-test rate. So the closest predicted average increase is points per additional practice test. Choice C.