Standard Form for the Equation of a Line
Another form for the equation of a line is standard form. Standard form
is useful, for example, when solving sytems of equations.
Definition
Standard Form for the Equation of a Line
The standard form for the equation of a line in two variables is
Ax + By = C, where A, B, and C are real numbers, and A and B are not both zero.
The following linear equations are written in standard form:
5x + 3y = 7
x  2y = 5 
Here, A = 5, B = 3, and C = 7.
Here, A = 1, B = 2, and C = 5 
Note:
When writing an equation in standard
form, the terms on the left must be
arranged in the form Ax + By. The xterm
is always written before the yterm.
2x + 5y = 3 is in standard form.
5y + 2x = 3 is NOT in standard form.
Example
Write the equation
in standard form.
Solution 
y + 4 

To clear the fraction, multiply both
sides of the equation by the LCD, 2. 
2[y + 4] 

Simplify. 
2y + 8 
= x  6 
Subtract 8 from both sides. 
2y 
= x  14 
Subtract x from both sides. 
x + 2y 
= 14 
The equation x + 2y = 14 is in standard form.
Here, A = 1, B = 2, and C = 14. 
