A Geometric Proof for a Theorem Estimating the Slope $\alpha$ of a Given Line L

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We have a theorem estimating the slope a of a given line $L$. This is done in terms of the slope of the point $P$ with coordinates $(q, p)$. The proof went through the case P is below $L$. Write up the proof for the case that $P$ is above $L$.

Here is the theorem and proof mentioned above (THE THEOREM IS TO BE THE BASIS OF MY PROOF, THE PROOF BELOW IS SIMPLY CONTEXT):

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I have not been able to solve this problem, and struggle to start. Can someone show the steps to a solution?