Question

If my tangent line at point (4,8) has the equation `y=5x/6 - 9`, what is the equation of the normal line at the same point?

Answer 1

The normal line is the line that is perpendicular to the the tangent line.

If the slope of a line is `m` then the slope of the perpendicular line is `-1/m`, this is also known as the negative reciprocal.

The given equation is `y=5/6x-9` the slope is `5/6` so the slope of the normal is `-6/5`.

The point `(x,y)->(4,8)`

`y=mx+b ->` Substitute in the values of `m`, `x` and `y`

`8=-6/5(4)+b`

`8=-24/5+b`

`24/5+8=b`

`24/5+40/5=b`

`64/5=b`

The equation of the normal line is `-> y=-6/5x+64/5`