Please help and explain.

$y=\frac{-2}{9}x+\frac{61}$

Step-by-step explanation:

For two lines to be parallel to each other, it means they have to have the same slope. So, the question is really asking for the line through $(8, 5)$ that has the same slope as the line shown.

We can start by finding the slope of the line shown. Recall that given two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$, the slope of the line between them is $\frac{y_{2}-y_{1}}{x_{2}-x{1}}$, or more commonly remembered as rise over run. Plugging in the points $(-3, 1)$ and $(6, -1)$ into the equation for the slope, we see that the slope of the line shown is $\frac{-1-1}{6-(-3)}=\frac{-2}{9}$.

We recall that the point-slope form of a line is such that given a point $(x_{1}, y_{1})$ and the slope $m$, the equation for a line with that slope through the given point is $y-y_{1}=m(x-x_{1})$(Note: divide by $x-x_{1}$. What does that remind you of?). Plugging in our point and slope, we have that the equation for the line we want is $y-5=\frac{-2}{9}(x-8)$. Expanding the right-hand side gives $y-5=\frac{-2}{9}x+\frac{16}{9}$.

Adding $5$ to both sides gives the desired $\boxed{y=\frac{-2}{9}x+\frac{61}}$

the function makes a strait line horizontally with no x intercept but a y intercept at 9.