Standard form of a line

Definition

The standard form of a line is an equation of the form $Ax + By = C$ where A, B, and C are integers, and A and B are not both zero. This form allows for easy identification of the x- and y-intercepts.

5 Must Know Facts For Your Next Test

1. The coefficients A, B, and C in the standard form equation $Ax + By = C$ are typically integers.
2. To convert from slope-intercept form ($y = mx + b$) to standard form, rearrange terms to get all variables on one side and constants on the other.
3. The x-intercept can be found by setting $y = 0$ in the equation $Ax + By = C$, resulting in $x = \frac{C}{A}$.
4. The y-intercept can be found by setting $x = 0$ in the equation $Ax + By = C$, resulting in $y = \frac{C}{B}$.
5. In standard form, if both A and B are zero simultaneously, it does not represent a valid line.

Related terms

Slope-Intercept Form: $y = mx + b$, where m represents the slope and b represents the y-intercept.

Point-Slope Form: $y - y_1 = m(x - x_1)$, used when you know a point $(x_1,y_1)$ on the line and its slope m.

Linear Function:

A function that graphs to a straight line; it has the general form $f(x) = mx + b$.