How to Find the Slope of a Nonlinear Line

By Kiran Gaunle
Slope measures steepness of a line.

Slope of a line is a measure of its steepness. Unlike a straight line, which has a constant slope, a nonlinear line has multiple slopes which depend on the point at which it is determined. For a continuous differentiable function, the slope is given by the derivative of the function at that particular point. In addition, the slope of the tangent drawn at a particular point in the nonlinear line is also its slope at that specific point.

Find Slope Using Derivative

Take the first derivative of the function whose slope you want to calculate. For example, for a line given by y = x^2 + 3x + 2, the first derivative equals 2x + 3.

Identify a point where you want to calculate the slope. Suppose the slope is being determined at the point (5,5).

Substitute the x value in the derivative to find the slope. In this example, 2 * 5 + 3 = 13. Therefore the slope of the nonlinear function y = x^2 + 3x + 2 at point (5,5) is 13.

Find Slope Using Tangent

Choose a point in the nonlinear line whose slope you want to calculate. Suppose you want to find the slope of the line at point (2,3).

Draw a line tangent to the point using a ruler.

Choose another point on the tangent and write its coordinates. Say, (6,7) is another point on the tangent line.

Use the formula slope = (y2 - y1)/ (x2 - x1) to find the slope at point (2,3). In this example, the slope is given by (7 - 3) / (6 - 2) = 1.

About the Author

Kiran Gaunle is a freelancer based in New York. He started writing professionally in 2006. He has written research reports for the UN Development Programme and the "Kathmandu Post." Gaunle is working on a book of short stories and a novel. He holds a Master of Arts in international political economy and development from Fordham University.