Question 699·Hard·Math

0 / 2000

Each dot in the scatterplot represents one student's number of tutoring sessions and score on a math assessment. A line of best fit is shown. Point $P$ represents one student.

For the student represented by point $P$ , by what percent is the actual assessment score greater than the score predicted by the line of best fit?

Do not include the percent sign in your answer.

Your answer

A line of best fit predicts a score, while a dot shows one student's actual score. If the question asks how much greater the actual score is, read the dot and use points on the line to find its prediction at the same input. Then divide the difference by the predicted score, not the actual score. Desmos can handle the slope and percent arithmetic.

Hints

Hint 1
A dot gives an actual score; the line gives a predicted score. At point $P$ 's number of tutoring sessions, which score comes from the dot, and which must come from the line?
Hint 2
The slope is the score change divided by the change in tutoring sessions. Use the two labeled points on the line, not point $P$ , to find how much the prediction rises per session.
Hint 3
A percent increase compares the extra amount with the starting amount. Here the predicted score is what the actual score is greater than, so put the predicted score under the difference.

Step-by-step

Read the line, then find the percent increase
Step 1
Separate the actual score from the line
Point $P=(6,81)$ is a student's dot, so $81$ is the actual score after $6$ tutoring sessions. The labeled points $(0,48)$ and $(9,84)$ lie on the fitted line, so use those to find what the line predicts. Don't use $P$ to find the line's slope: the dot sits above the line.
Step 2
Find the line's score change per session
The slope is the change in score divided by the matching change in sessions. Type $\frac{84-48}{9-0}$ in Desmos. It returns $4$ , so the line's predicted score rises $4$ points per session.
Step 3
Find the prediction at six sessions
The line predicts $48$ points at $0$ sessions and adds $4$ points for each session. Add $4(6)+48$ in Desmos. It returns $72$ , the predicted score at $6$ sessions. Keep this separate from the dot's actual score of $81$ .
Step 4
Compare the difference with the prediction
“Actual score greater than predicted” asks for a percent increase from the prediction to the actual score. Divide by the predicted score, the amount you're comparing against. So the percent is $\frac{81-72}{72}\times100$ . Dividing by $81$ instead would compare the difference with the actual score.
Step 5
Calculate and grid in the percent
Type $\frac{81-72}{72}\times100$ in Desmos. It returns $12.5$ , so the actual score is $12.5\%$ greater than the predicted score. Enter the number without a percent sign. Grid in 12.5.

Question 699·Hard·Math

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this