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.
Find Slope Using Derivative
Step 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.
Step 2
Identify a point where you want to calculate the slope. Suppose the slope is being determined at the point (5,5).
Step 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
Step 1
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).
Step 2
Draw a line tangent to the point using a ruler.
Step 3
Choose another point on the tangent and write its coordinates. Say, (6,7) is another point on the tangent line.
Step 4
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.
Cite This Article
MLA
Gaunle, Kiran. "How To Find The Slope Of A Nonlinear Line" sciencing.com, https://www.sciencing.com/slope-nonlinear-line-8353770/. 24 April 2017.
APA
Gaunle, Kiran. (2017, April 24). How To Find The Slope Of A Nonlinear Line. sciencing.com. Retrieved from https://www.sciencing.com/slope-nonlinear-line-8353770/
Chicago
Gaunle, Kiran. How To Find The Slope Of A Nonlinear Line last modified March 24, 2022. https://www.sciencing.com/slope-nonlinear-line-8353770/