Question

How do you draw the slope field of the differential equation `y'=y-x` ?

Answer 1

You have to substitute values of `x` and `y` into your differential equation. The result will be the value of `y'` which represents the slope in that point of your function (solution of your differntial equation).
To draw these slope field may be a little bit challenging but you can use softwares that can help you to do that, such as the one from:
http://www.mathscoop.com/calculus/differential-equations/slope-field-generator.php

In your case you may use pencil and paper and draw at each point a little line with inclination representing the value calculated at that point.
Have a look at the drawing obtained from the above website using your equation:

Consider, for example, the coordinates:
`x=2` and `y=2`
You get `y'=y-x=2-2=0`
This means `slope=0` and you'll draw a vertical line (red circle in the next picture):

By hand you can draw less lines and speed up a little bit the process but I would suggest you to use the help of a software anyway.