Question

practice:

1. which equation would be the most accurate line of best fit for the scatter plot?

scatter plot image
a ( y = -x + 9 )
b ( y = \frac{1}{2}x + 9 )
c ( y = -\frac{2}{3}x )
d ( y = -\frac{1}{2}x + 9 )

Explanation:

Step1: Analyze the trend of the scatter plot

The scatter plot shows a negative correlation (as x increases, y decreases), so the slope should be negative. This eliminates option B (positive slope $\frac{1}{2}$).

Step2: Analyze the y - intercept

Looking at the scatter plot, when x = 0, the y - value is around 9. Option C has a y - intercept of 0, which does not match. So we can eliminate option C.

Step3: Analyze the slope magnitude

Option A has a slope of - 1, and option D has a slope of $-\frac{1}{2}$. The points in the scatter plot do not show a very steep decrease (a slope of - 1 would be a steep negative line). The more gradual negative slope of $-\frac{1}{2}$ in option D better fits the trend of the scatter plot.

Answer:

D. $y = -\frac{1}{2}x + 9$