How to Find the Slope of a Nonlinear Line

Find Slope Using Derivative

• 1

  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.

• 2

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

• 3

  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

• 4

  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).

• 5

  Draw a line tangent to the point using a ruler.

• 6

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

• 7

  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.