Standard Form of a Line

There are many ways to write a linear equation (an equation that represents a line).  When we graph a line, we like to put it in $y=mx+b$ form, because that makes it easy to find the slope and the y-intercept.  But, lines can also be given in standard form. 

Standard form is: 

$Ax+By=C$

Essentially the $x$ term comes first, added to the $y$ term, equal to the number (which we call $C$).

Standard form is especially helpful when you want to find the x- and y-intercepts of a line.  It is easy to zero out one variable and find the value of the other when they are both on the same side of the equation.

To rearrange an equation into standard form, you just follow algebra rules (whatever you do to one side of the equation, you do to the other).  Remember, you can combine like terms when they are on the same side of the equation.

Example:

Put the following equation in standard form: $4y-2=x$

$$\eqalign{4y-2&=x\qquad &&\text{We want to move the x term to the left and the number to the right}\\+2 & \quad+2 &&\text{Add two to each side}\\4y&=x +2\\-x&\;\;-x&&\text{Subtract x from each side}\\-x+4y&=2&&\text{Equation is in standard form}}$$

Bottom line, to put a linear equation into standard form, combine like terms on the same sides of the equal sign, then use balance (what you do to one side, you do to the other) to move terms into $Ax+By=C$ form.