Take a look at the applet: Linear Relations
An equation of the form $ax+by=c$ describes a linear relationship with two variables. The corresponding graph is a straight line. You can find this graph by determining points along this line. This is often done by choosing $x=0$ and calculating the corresponding value for $y$, and by then choosing $y=0$ and calculating the corresponding value for $x$.
Linear equations with two variables such as
$ax+by=c$ can be rewritten as a linear function as long as
$b\ne 0$.
For example the equation
$2x+3y=6$ can be reorganised to give
$y=\mathrm{-}\frac{2}{3}x+2$.
This is then a linear function with
`y`
-intercept
$2$ and gradient
$\mathrm{-}\frac{2}{3}$.
Special cases:
$a=0$: the equation then takes on the form $by=c$ and can be rewritten as $y=\frac{c}{b}$. This is a linear function with gradient $0$.
$b=0$: the equation takes on the form $ax=c$ and can be rewritten as $x=\frac{c}{a}$. This is not a linear function as there is no gradient. The graph is a line parallel to the $y$ -axis.