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

Jan 21, 2015

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 $s l o p e = 0$ 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.