What is the equation of a line through point (-4,5) that is perpendicular to the line with equation y=-6x+4?

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