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# 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 x-term is always written before the y-term.

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.