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If we find the slope of a line via two point form we find that when the for different points in the same straight line we have different equations. Why is it so? Say, if the points were $3,5$ and $6,10$ then the equation was $2x-y=1$ and when the points were $4,6$ and $6,11$ then the equation of line was $2x-y=2$. Why this deviation?

Gerry Myerson
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Arj
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    $(6,10)$ is not on the line $2x-y=1$. $(6,11)$ is not on the line $2x-y=2$. – lulu Oct 14 '15 at 05:28
  • Also, the line through $(3,5)$ and $(6,10)$ isn't the same as the line through $(4,6)$ and $(6,11)$, so it's not surprising that it doesn't have the same equation. – Gerry Myerson Oct 14 '15 at 06:11

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The two st lines you mentioned are compeltely different so of course you will have two different equations !!

For the first one passing through $ (3,5)$ and $(6,10)$, its equation is $y=5/3x$.

For the second one passing through $ (4,6)$ and $(6,11)$, its equation is $ y=5/2x-4$. Here is their plot : enter image description here

Nizar
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