Standard form

Standard form is a way to write linear equations given by the equation:

Ax + By = C

where A, B, and C are constants.

Standard form is useful because you can easily identify x- and y-intercepts of the line.

However, because standard form does not include the slope m, it is much easier to write a linear equation in slope-intercept or point-slope form first, then convert it to standard form. when graphing linear equations, it is easier to use slope-intercept or point-slope form.

In standard form, the x-intercept of the line is . This is because if you set y = 0, then .

The y-intercept of a linear equation in standard form is . This is because if you set x = 0, then .

Example

3x + 2y = 6

3x + 2(0) = 6 3(0) + 2y = 6
3x = 6 2y = 6
x = 2 y = 3
x-intercept at (2, 0) y-intercept at (0, 3)

When solving systems of equations, it is common for you to see linear equations written in standard form.


See also system of equations.