If a line passes through the point (3, 5) and has a positive slope

A line has a positive slope when it moves from the 3rd Quadrant to the 1st quadrant
Please refer to the attached graph. The point shown is \((3,5)\)


We can see that the \(y\)-intercept can satisfy all of the three options.

I. \(c < 0,\hspace{2mm} \) need not necessarily be true as \(c=0,\) e.g. line \(2\) and \(c>0\) e.g.line \(1\) are also possible.
II. \(c = 0,\hspace{1mm} \) need not necessarily be true as \(c >0,\) e.g. line \(1\) and \(c<0\) e.g.line \(3\) are also possible.
III. \(c>0,\hspace{0mm} \) need not necessarily be true as \(c =0,\) e.g. line \(2\) and \(c< 0\) e.g.line \(3\) are also possible.

Ans E

Hope it's clear


Thank you, seems there was an issue with my external HDD. Saved image to system HDD and was able to upload.
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Since all three are possible why can't the answer choice be option D?

This is because the question asks "which of the following MUST be true," not "which of the following COULD be true," and while each option could be true, none of them is necessarily true.
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