# How do you draw slope fields?

May 10, 2018

Example:

How do you draw the slope field for $\frac{\mathrm{dy}}{\mathrm{dx}} = x - y$?

The slope field is a cartesian grid where you draw lines in various directions to represent the slopes of the tangents to the solution. Therefore by drawing a curve through consecutive slope lines, you can find a solution to the differential equation.

Take the example of $\frac{\mathrm{dy}}{\mathrm{dx}}$ at $\left(3 , 4\right)$. Here we see that

$\frac{\mathrm{dy}}{\mathrm{dx}} = 3 - 4 = - 1$

So you would draw a line of slope $- 1$ at $\left(3 , 4\right)$. Repeat this for maybe 4 by 4 points to get the following slope field

Hopefully this helps!