Slope-intercept form is:
y = mx + b
"m" is the slope, "b" is the y-intercept (the y value when x = 0)
(there is probably another way to do this, but I will be doing it this way)
Isolate the "y" in the equation
3x + 4y = 12 Subtract 3x on both sides
4y = 12 - 3x Divide 4 on both sides
[tex]y=3-\frac{3}{4}x[/tex] or [tex]y=-\frac{3}{4} x+3[/tex] The slope is -3/4
For lines to be parallel, they have to have the SAME slope. The given line's slope is -3/4, so the slope of the parallel line is also [tex]-\frac{3}{4}[/tex]
