Find the slope-intercept form of the line passing through the point (7, -2) and parallel to the line y=-8x-4?
$\displaystyle y-y_{1}=m(x-x_{1})$ is the point-slope form of a line. I mention this one first because we are given a point on a line and told to find it's equation. All we lack is a slope.
We are told though, that this particular line is PARALLEL to the line defined as $\displaystyle y=-8x-4$. To be parallel means that our two lines have the same slope correct? Knowing that, we have the slope of $\displaystyle y=-8x-4$ as $\displaystyle -8$ and we can then plug that back into our point-slope form of a line.
All that is left to do at this point (no pun intended) is to put it into slope-intercept form.
Since the line is parallel to y=-8x-4, it has the same slope.
Now, since we have the slope m, and a point it passes through, we can solve for the y-intercept, b, and that's it.
$\displaystyle -2=-8(7)+b$
Solve for b and then set up the slope intercept form, y=mx+b