Consider the graph of the  linear equation $2x-4y=12$. 

Since $(0,\text-3)$ is a point on the graph of the equation, $(0,\text-3)$ is a solution to the equation. Any point not on the line is not a solution to the equation. 

Sometimes the coordinates of a solution cannot be determined exactly by looking at the graph. For example, when $x=1.5$, the $y$-value is somewhere between -2 and -3. If we have a value for one of the variables, we can use the equation to figure out the value of the other variable.

$\begin{aligned}2x-4y&=12 \\2(1.5)-4y&=12 \\3-4y&=12\\\text-4y&=9\\y&=\text-\frac94\text{ or } \text- 2\frac14\end{aligned}$

The equation can also be used to check whether a pair of values is a solution to the equation by seeing if the values make the equation true. For example, since the values $x=5$ and $y=2$ do not make the equation true, then the point $(5,2)$ is not a solution and does not lie on the line.