How to Find the Slope of a Nonlinear 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.

Things You'll Need

  • Ruler (optional)

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.


  • Photo Credit Jupiterimages/Brand X Pictures/Getty Images
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