what will the y - value be when the x - value is 8?

Explanation:

Step1: Find the slope - intercept form

The line passes through the points $(0, 1)$ and $(- 2,-2)$. The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1=1,x_2=-2,y_2 = - 2$, so $m=\frac{-2 - 1}{-2-0}=\frac{-3}{-2}=\frac{3}{2}$. The y - intercept $b$ is the y - value when $x = 0$, so $b = 1$. The equation of the line is $y=mx + b=\frac{3}{2}x+1$.

Step2: Substitute $x = 8$

Substitute $x = 8$ into the equation $y=\frac{3}{2}x + 1$. Then $y=\frac{3}{2}\times8+1$. First, calculate $\frac{3}{2}\times8=12$, then $y=12 + 1=13$.

Answer:

13