#  >> K-12 >> AP Classes

How to Graph Slope Fields

Solving differential equations is a central concept in high school and college calculus courses, which makes understanding such problems critical to success. Slope fields can be used as a graphical method for solving differential equations and the ability to sketch a slope field often appears on test questions -- including on the Advanced Placement (AP) Calculus exam. Learning how to create a slope field can help you solve differential equation problems in higher level coursework as well as improve your test scores on AP, dual enrollment, or college exams.

Instructions

    • 1

      Identify the differential equation that you will be using to create your slope field. Differential equations are usually expressed as equal to dy/dx or a derivative such as y' or f'(x). If you're given an equation in a different form, you may need to differentiate or integrate it first.

    • 2

      Draw a coordinate plane. Your plane should extend three to five points outward each direction on both the x-axis and y-axis. On tests, the coordinate plane will often be provided for you.

    • 3

      Plug coordinate points into the differential equation. Substitute the x-coordinate for x and the y-coordinate for y in the equation and solve for the numerical value. The solution is the slope of the equation at that point. For example, plugging in the point (1,1) to the equation dy/dx = x + y yields a solution of 2. Repeat this step for each coordinate on the plane.

    • 4

      Sketch the slope of the equation at each point on the coordinate plane. If the slope of the equation at (1,1) is 1, for example, draw a small line with a perfectly diagonal slope at the point (1,1). If the slope at (-1,1) is 0, draw a flat line at the point (-1,1). Repeat this step for each point on the coordinate plane. After each point on the plane has a slope, you have completed the slope field.

Learnify Hub © www.0685.com All Rights Reserved