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$A$'s coordinates are $(6,5)$ and $B$'s are $(2,-1)$. I have tried time and time again to do this but keep ending up with $c$ (from $y=mx + c$) as $-4$ when it should be $8$, can anyone help?

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You did it right.

$3x-2y = 8 \Longrightarrow -2y = 8-3x \Longrightarrow y = \frac{3}{2}x-4$

Your only mistake was that you didn't work the above chain "backwards" to show that your $y=mx+b$ form is equivalent to what is sometimes called the "parametric form" of a line: $c_1x+c_2y = k$.

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    ive never been taught that so thats really helpful!2012-09-18