Question

How do you find the slope of a line parallel to `2y=6x+18`?

Answer 1

If you divide both sides of this equation by `2` you get:

`y = 3x+9`

This is the equation of the line in slope-intercept form, with slope `m=3` and intercept `c=9`.

Any line parallel to it will have the same slope, `3`.

Incidentally, any line perpendicular to a line of slope `m` will have slope `-1/m`. So in your case, any line perpendicular to your line will have slope `-1/3`.