Question

write an equation for the specific line: through (4,-12) and parallel to 4x+3y=12

Answer 1

4x+3y=-20

Answer 2

parallel=same slope ,y=mx+b m= -4/3x , (4,-12)
-12=-4/3(4) +b
-12=-16/3+b
-36/3+16/3=b
-23/3=b
so y=-4/3x-23/3

Answer 3

solve 4x + 3y = 12 for y... so that it is in (y = mx + b) form...

4x + 3y = 12

minus 4x from each side and get:

3y = -4x +12

divide by 3 on both sides and that will be

y = (-4/3)x + 4 which is the y = mx + b form... now you can see what m is...
so now you know the slope is (-4/3) = m

So you can use the point slope formula which is y - y1 = m(x -x1)
you know the point is (4 -12) and you know m is (-4/3)
so the equation is using point slope is

y - (-12) = (-4/3)(x - 4)

now solve...
first distribute the (-4/3)

y+12 = (-4/3)x + (16/3) {two neg. = pos}

subtract 12 to both sides

y = (-4/3)x + (16/3) - 12
y = (-4/3)x - 20/3

unless I made an error somewhere. foo! that was fun.