# Different forms of linear equations

1. Apr 15, 2006

### Beam me down

A while back in maths we were introduced to the linear equation in two forms:

$$a x + b y = c$$ (1)

$$y = m x + c$$ (2)

Now I can use both forms of these, but I was told that:

$$y = m x + c \Leftrightarrow a x + b y = c$$

where $$m = \frac{a}{b}$$

Thiis can't be right can it? As:

$$a x + b y = c$$

$$b y = c - a x$$

$$y = \frac{c}{b} - \frac{a x }{b}$$

Last edited: Apr 15, 2006
2. Apr 15, 2006

### Astronuc

Staff Emeritus
Obviously the c's in equations 1 and 2 are not the same. They cannot be as you have demonstrated.

Using $$y = \frac{c}{b} - \frac{a x }{b}$$

and $$y = m x + d$$,

then m = $$-\frac{a}{b}$$ and

d = $$\frac{c}{b}$$

3. Apr 15, 2006

### Beam me down

Thanks. My teacher was saying the two forms are the same (ie: at least "c" in both equations are the same). I couldn't prove it, and nor could she, and we both forgot about it.

4. Apr 15, 2006

### Astronuc

Staff Emeritus
Both equations represent a line, but the coefficients must be numerically different.

Basically, one is dividing all terms in (1) by the coefficient (b) of y, and to be equal, the m = - (a/b) and c in equation 2 must be c/a, so the c's must be different.