I am studying Diophantine equations, and I don't understand the underlined portion of my attachment. (Attached in my next post)

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I am studying Diophantine equations, and I don't understand the underlined portion of my attachment. (Attached in my next post)

Mathematics
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Here is my attachment. Please help.
1 Attachment
change q back into b/d and see what happens?
Hello.

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Hello, did you decide to abandon me? :)
??
Remember you promised to look into those problems in this weekend
Oh - I have been preoccupied. I'll look tomorrow. I can help you with this one now, though.
I thought I did something wrong, perhaps said something I shouldn't have said, or something of that sort.
No, you need to calm down :) I keep saying that.
Do you want the answer to this one? ;)
Or have you figured it out already?
Yes ofcourse,
Is that a thing to ask? :)
No I haven't figured out anything
Okay...look at the equation you get,\[p(x-x_0)+q(y-y_0)=0\]then\[(y-y_0)=-\frac{p(x-x_0)}{q}\]The left-hand side is an integer, and you're told that p and q are relatively prime, so for the right-hand side to remain an integer, it must be that q divides (x-x_0).
What an idiot I am
a(x-x0)+b(y-y0)=0 b(x-x0) = -a(y-y0) b/d=q; a/d=p q(y-y0) = -p(x-x0) (y-y0) = -p (x-x0)/q y-y0 =
Thinking over this for the last 1 hour but didn't figure this thing out
Just keep thinking of NUMBERS. These equations are about NUMBERS.
Yeah, I understand it now. Infact as I told, I should have figured this thing myself. But couldn't
I mean it is simple enough
And I shouldn't have asked it
Anyhow thanks thanks thanks thanks both of you
yw
np :)
Anyhow - I need sleep.

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