Suppose we have a line that is tangent to a curve at a point P. The normal line to the curve at P is the line perpendicular to the tangent line at P. The concept of the normal line is used throughout math and science. How can we determine the equation of a normal line?

Recall from basic geometry that the product of the slopes of two perpendicular lines is equal to -1.

Therefore, the slope of the normal line is equal to the negative reciprocal of the slope of the tangent line.

To determine the slope of the tangent line at point P, we first determine the slope equation by taking the derivative of the curve function.

We then substitute the x value for the point P into the slope equation.

The slope of the normal line at point P is the negative reciprocal of the tangent slope.

To determine the equation of the normal line, we substitute the calculated slope and the coordinates at P into the point-slope formula.

After some rearranging, we have the equation for the normal line.

Here is the graph of another function, and a normal line to the curve at point P.

What is the equation of the normal line to the curve at point P? Click the "Submit" button after selecting your answer.

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