A line perpendicular to another line will have a slope that is the negative reciprocal of the slope of that line. This means that, if Line 1 has a slope of m, a perpendicular
Line 2 will have a slope of -1/m.
Line y = -3x + 4 has a slope of -3. A line perpendicular to it should have a slope of –(1/-3) = 1/3, with an equation in the form: y = x/3 + b
Only the Line y = x/3 + 3 is similar to this format. To make sure that it is the correct equation of the perpendicular line, plug in (3, 4) to solve for b:
y = x/3 + b
4 = 3/3 + b
b = 4-1 = 3
Therefore, the correct equation is y = x/3 + 3