Question: How to plot a linear transformation

The problem is how to plot a linear transformation, for example,

(x,y)->(x-y/2,y)

As, I searched, I found out that the code "LinearTransformPlot" can do that but it defines to act for example on lines or a certain subspace. May I ask you to learn the solution. Should we have a subspace untill we can plot the transformation? Thanks

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