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Can Mathematica produce a sheet of virtual graph paper on which user can draw points and lines using the mouse?

Some background for this question:

I am taking a course at Coursera and the professors draw lines and notations on some kind of "blackboard" that is shown in the video (a screen shot is shown below).

Would it be possible to have similar drawing functionality in Mathematica but with a graph paper background?

coursera screen shot

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Have you seen the basic drawing tools? e.g. starting from 

Graphics[{},
 GridLines -> Transpose@Table[{x, x}, {x, -10, 10, 0.08}],
 Frame -> True,
 PlotRange -> {{-1, 1}, {-1, 1}/GoldenRatio},
 ImageSize -> {1000, 1000/GoldenRatio}
 ]

and then right-clicking on the graphics and choosing "drawing tools" will give you something like what you are asking for. It's a little bit finicky to work with, to be honest, but it's there. (You can see in the screen recording below, for example, that I had trouble setting the color for the last character for some reason.)

enter image description here

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