a scatter plot is shown below. a line of best fit passes through point a and another point in the data set…

Explanation:

Step1: Assume point A is (2, 3). Visually estimate another point on line of best - fit.

Let's assume another point on the line of best - fit is (6, 5) (a point that seems to lie on the trend line passing through A).

Step2: Find the slope of the line.

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using $(x_1,y_1)=(2,3)$ and $(x_2,y_2)=(6,5)$, we have $m=\frac{5 - 3}{6 - 2}=\frac{2}{4}=\frac{1}{2}$.

Step3: Use the point - slope form of a line $y - y_1=m(x - x_1)$ to find the equation of the line.

Using $(x_1,y_1)=(2,3)$ and $m = \frac{1}{2}$, we get $y-3=\frac{1}{2}(x - 2)$. Expanding, $y-3=\frac{1}{2}x-1$. Then $y=\frac{1}{2}x + 2$.

Step4: Find the value of y when x = 9.

Substitute $x = 9$ into $y=\frac{1}{2}x + 2$. So $y=\frac{1}{2}\times9+2=\frac{9}{2}+2=\frac{9 + 4}{2}=\frac{13}{2}=6.5$.

Answer:

6.5