Question

How do you draw slope fields?

Answer 1

Example:

How do you draw the slope field for `dy/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 `dy/dx` at `(3, 4)`. Here we see that

`dy/dx = 3 - 4 =-1`

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

Hopefully this helps!