The standard form of a line is ax+by=c, so we must get both variables on one side of the equal sign and a constant on the other...
y-4=(3/4)(x+8) perform indicated multiplication on right side
y-4=(3x+24)/4 multiply both sides by 4
4y-16=2x+24 add 16 to both sides
4y=2x+40 subtract 2x from both sides
-2x+4y=40 (note that by convention, coefficient of x should be positive) divide both sides by -1
2x-4y=-40
