solve for y by subtracting x from each side
4y = -x + 12
now divide each side by 4
y = -1/4 x +3
this is the slope intercept form of the equation
the slope is -1/4 and the y intercept is 3
The slope-intercept form:
[tex]y=mx+b[/tex]
We have x + 4y = 12:
[tex]x+4y=12\qquad|\text{subtract x from both sides}\\\\4y=-x+12\qquad|\text{divide both sides by 4}\\\\\boxed{y=\dfrac{-x+12}{3}=-\dfrac{1}{4}x+3}[/tex]