Slope fields

To graph a slope-field in Mathematica, you use the command PlotVectorField.  The "vector field" you are actually plotting has the coordinates at each point (since each vector goes "over" 1 and "up" by the slope).  So, to graph the slope field for:  

To clean it up a bit and make it look nicer, try the following options:

If you prefer to make all of the vectors have the same length, try the following:

It's a bit complicated how the options work, but if you play around with those numbers a bit you can get something that looks quite nice (be sure that you copy ScaleFunction exactly and then play with the number only; the & is very important).