Find equation of a straight line I have the question: Find in the form $ax+by+c=0$, where $a, b$ and $c$ are integers, the equation of the straight line which passes through each pair of points, given by  $(3,0)$ and $(5,2)$
I have worked this out up to $y = x - 3$ , but I am unsure as to whether the final answer should be $x-y-3=0$ by bringing the $y$ to the other side or whether it should be $y-x+3=0$.
 A: 
I am unsure as to whether the final answer should be $x-y-3=0$ by bringing the $y$ to the other side or whether it should be $y-x+3=0$.

Either solution is correct. If you want to follow the given form more to the letter, you might write your second alternative as $(-1)x+1y+3=0$ to preserve the order of coefficients. The first form would be more explicit as $1x+(-1)y+(-3)=0$, too, but I doubt anyone would actually have trouble reading these coefficients from either of your equations.
The parametrization of the line as you gave it is homogeneous, since scaling the equation by any non-zero factor describes the same object. So both the equations above describe the same line, and the equation $3x-3y-9=0$ would still describe the same line.
Formally one could consider $(a,b,c)$ as a coordinate vector, and then consider equivalence classes of all the non-zero multiples of such a vector. The result would be projective space, where each line is represented by homogeneous coordinates. These coordinates are also often written as $[a:b:c]$, with the square brackets indicating (to some) that these are in fact equivalence classes, and with the colons indicating (to some) that the absolute values are irrelevant, it's the ratios between them which describe the object.
