Need help with relatively simple linear programming

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It seems that question is asking for me to form a straight line that has the steepest gradient? But I kinda doubt this because we wouldn't need linear programming to do that, just a simple gradient calculator could do that.

So far all I can do is substitute each of the 3 coordinates to obtain

a+b=1
3a+b=2
4a+b=3

But this doesn't seem to make much sense.