to find the gradient of the perpendicular line, we know that we must do the negative inverse of the current line's gradient
-6x from the old line will now be 1/6x
we are given points on that line and we therefore use the points and the new gradient to find the equation of the line using this formula
y-y1=m(x-x1) where m is the gradient
input the values that we have
y-5=1/6(x--4)
rearrange
y-5=1/6(x+4)
y-5=1/6x+4/6
6y-30=x+4
6y=x+34
y=1/6x+34/6
y=1/6x+17/3
