How do you draw slope fields?

esempio:

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.

Prendi l'esempio di #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

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