# Slope Fields

## Key Questions

• 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!

• If you are allowed to use a software, then a software called GeoGebra gives us the slope field below.

I hope that this was helpful.

• Slope field can be used to visualize the flow of the solution curves of its corresponding differential equation. At each point of the solution curve, the curve will have the slope indicated in the slope field.