Express each of the following equations in the form ax + by + c = 0 and indicate the values of a, b, c in each case.
(i) x = 6
(ii) 3x – y = x – 1
(iii) 2x + 9 = 0
(iv) 4y = 7
(v) x + y = 4
(vi) $\frac{x}{2} - \frac{y}{3} = \frac{1}{6} + y$

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Solution

(i) x = 6
In the form of ax + by + c = 0 we have $x + 0 y + (- 6) = 0$ where a = 1, b = 0 and $c = - 6$ .
(ii) 3x – y = x – 1
In the form of ax + by + c = 0 we have $2 x + (- 1 y) + 1 = 0$ where a = 2, b = $- 1$ and c = 1
(iii) 2x + 9 = 0
In the form of ax + by + c = 0 we have $2 x + (- 1 y) + 1 = 0$ where a = 2, b = $- 1$ and c = 1
(iv) 4y = 7
In the form of ax + by + 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 ax + by + 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 ax + by + c = 0 we have $3 x - 2 y = 1 + 6 y \Rightarrow 3 x - 8 y + (- 1) = 0$ where $a = 3, b = - 8, c = - 1$ .

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