Express each of the following equations in the form ax + by + c = 0 and indicate the values of a, b, c in each case.

Solution:

(i) x = 6

In the form of $a x+b y+c=0$ we have $x+0 y+(-6)=0$ where $a=1, b=0$ and $c=-6$

(ii) $3 x-y=x-1$

In the form of $a x+b y+c=0$ we have $2 x+(-1 y)+1=0$ where $a=2, b=-1$ and $c=1$

(iii) $2 x+9=0$

In the form of $a x+b y+c=0$ we have $2 x+(-1 y)+1=0$ where $a=2, b=-1$ and $c=1$

(iv) $4 y=7$

In the form of $a x+b y+c=0$ we have $0 x+4 y+(-7)=0$ where $a=0, b=4$ and $c=-7$

(v) $x+y=4$

In the form of $a x+b y+c=0$ we have $1 x+1 y+(-4)=0$ where $a=1, b=1, c=-4$

(vi) $\frac{x}{2}-\frac{y}{3}=\frac{1}{6}+y$

In the form of $a x+b y+c=0$ we have $3 x-2 y=1+6 y \Rightarrow 3 x-8 y+(-1)=0$ where

$a=3, b=-8, c=-1$