# How do you find the equation of a normal line to a curve at a given point?

##### 1 Answer

The equation of a normal line will have the form

and its slope will be the negative reciprocal of the curve's derivative at the point. That is to say, take the value of the derivative at the point, divide 1 by it, and then multiply that value by

This is much better illustrated with an example:

Let's say that we are expected to find the equation of a line normal to the curve

The negative reciprocal of

The last step is to plug in the coordinates of our point and solve for

Now we have everything needed to put our full equation together: