Often, for equations, you want to find the slope of the equation. This way of writing the equation makes it easy to know the slope - the slope of this line is m.

The equation y = x is written in this form. This indicates that the slope of this equation is 1. The same equation can be written as x - y = 0. However, it is not evident what the slope of the equation x - y = 0 is from the equation.

This form of the equation also makes it easy to find out the y-intercept - it is b in this case.

Another common form of writing an equation is \frac{x}{a}\ +\ \frac{y}{b}\ =\ 1. If an equation is written in this form, the x-intercept is a and the y-intercept is b.

Different forms of the equation are created just to make it easy to find out important properties of lines like x-intercept, y-intercept and slope.

Given the equation x+y=2, what is the x-intercept, y-intercept and slope?

Divide this equation by 2 and write the same equation as \frac{x}{2}+\frac{y}{2}=1 to get x-intercept as 2 and y-intercept as 2.

Take x to the other side to get, y=-x\ +\ 2 to get the slope as -1 for this equation.

Both are techniques that make it easy to figure out properties of the line easily.