Hey there! :)
3y + 2x = 12
To find the slope of this equation, we must turn this into slope-intercept form. Slope-intercept form is very simply : y = mx + b ; where m = slope, b = y-intercept.
Our first step should be to subtract 2x from both sides.
3y + 2x - 2x = 12 - 2x
Simplify.
3y = -2x + 12
Then, divide both sides by 3 so that we could get y by itself (which is what we call isolated in the math world).
3y ÷ 3 = (-2x + 12) ÷ 3
Simplify.
y = -2/3x + 4
So, our slope is -2/3!
~hope I helped~