Currently the equation 6x - 2y = 18 is in standard form. Convert the standard form equation into a slope-intercept form and we can find the slope easily.
Solve for y.
6x - 2y = 18
-2y = 18 - 6x <-- Subtract 6x from each side. This is to isolate the 2y term
2y / -2 =
<-- Divide each side by 2. This it to
get rid of the 2 coefficient.
y = -9 + 3x
Rearrange the right-hand side a bit.
y = -9 + 3x becomes y = 3x - 9
Now it is in slope-intercept form.
The slope is the coefficient of the x variable.
So, 3 is the slope.