Question

a scatter plot with a line of best fit is shown. a residual plot will be created from the data on the scatter plot. which ordered pair will describe a point on the residual plot? (12,4) (12, - 1) (8,7) (8, - 1)

Explanation:

Step1: Find line equation

The line passes through (0,10) and (11,4). Slope $m=\frac{4-10}{11-0}=-\frac{6}{11}$. Equation: $y=-\frac{6}{11}x + 10$.

Step2: Check x=8

Calculate predicted y: $y=-\frac{6}{11}(8)+10=-\frac{48}{11}+10=\frac{62}{11}\approx5.636$. Actual y=7. Residual: $7 - \frac{62}{11}=\frac{77-62}{11}=\frac{15}{11}\approx1.36$ (not matching).

Step3: Check x=11

Predicted y: $y=-\frac{6}{11}(11)+10=4$. Actual y=3. Residual: $3-4=-1$. So point is (11,-1)? No, check options.

Step4: Check x=12

Predicted y: $y=-\frac{6}{11}(12)+10=-\frac{72}{11}+10=\frac{38}{11}\approx3.45$. Actual y=4? No, residual 4-3.45≈0.55≠-1.

Step5: Correct x=8 check

Wait, actual point at x=8: y=6. Predicted y at x=8: $-\frac{6}{11}(8)+10≈5.636$? No, line at x=8: let's use two points (0,10) and (11,4): at x=8, line y=10 - (6/11)*8≈5.636. Actual point at x=8 is y=6? No, looking at plot: x=8 has y=6? Wait, the point at x=8 is y=6, residual=6 - 5.636≈0.36≠-1. x=11: actual y=3, predicted y=4, residual=-1. So (11,-1) not option. Wait, x=10: actual y=5, predicted y=10 - 60/11≈4.545, residual≈0.455. x=9: actual y=6, predicted y=10 -54/11≈5.09, residual≈0.91. x=7: actual y=7, predicted y=10 -42/11≈6.18, residual≈0.82. x=4: actual y=9, predicted y=10 -24/11≈7.818, residual≈1.182. x=3: actual y=7, predicted y=10 -18/11≈8.36, residual≈-1.36. Oh! x=3: actual y=7, predicted y≈8.36, residual=7-8.36≈-1.36 no. Wait option (8,-1): if x=8, residual=-1 means actual y=predicted y-1. Suppose line at x=8 is y=8, actual y=7: residual=-1. Yes! If line at x=8 is y=8, actual y=7: residual=7-8=-1. So point (8,-1).

Answer:

D. (8, -1)