Slope fields are a graphical representation to the solution of a differential equation.

To plot a slope field, you only need to plug-n-chug.

1. Make a coordinate grid (any scale you like) and fill it with dots at (x, y) coordinates.
2. Pick a (x, y) coordinate and plug it into your differential equation (where dy/dx = some equation). This will give you the value of the slope $m$
3. At that (x, y) coordinate, plot a very short line of slope $m$. The line should be very short and should not touch any other coordinate.
4. Repeat steps 2 and 3 for every (x, y) coordinate in your grid

This can be a time consuming process.