Perindicular lines have a slope which is the negative reciprocal of the other slope. So instead of - 1/3, it will have a slope of 3. Now we have y=3x+b but we need to solve for b. If it goes through the point (1,5) set y to 5 and x to 1 then solve for b
5=3(1)+b so then b=2 and we have the equation y=3x+2