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# Standard Form for the Equation of a Line

When we wrote the equation of a line in point-slope form, the equations looked different depending on the point we chose. To show that the equations are equivalent, rewrite each equation in standard form.

Definition â€” Standard Form for the Equation of a Line

The standard form for the equation of a line is Ax + By = C Where A, B, and C are real numbers and A and B are not both zero.

To write the equation of a line in standard form, move the terms with variables to the left side and the constant term to the right side of the equation.

Example 1

We can find the equation of the line that passes through the points (-2, 7) and (6, 3).

We may use the point (6, 3) to obtain: If we instead use (-2, 7), we obtain: a. Write in standard form.

b. Write in standard form.

c. What conclusion can you draw?

Solution

In each case, we want the x-term and y-term on the left side of the equation. We want the constant term on the right side of the equation.

 a. To clear the fraction, multiply both sides by 2. 2 Â· (y - 3) Simplify. Distribute -1. Add x to both sides. Add 6 to both sides. 2y - 6 2y - 6 x + 2y - 6 x + 2y = -1(x - 6) = -x + 6 = 6 = 12 b. To clear the fraction, multiply both sides by 2. 2 Â· (y - 7) Simplify. Distribute -1. Add x to both sides. Add 14 to both sides. 2y - 14 2y - 14 x + 2y - 14 x + 2y = -1(x + 2) = -x - 2 = -2 = 12
c. In standard form, each equation is x + 2y = 12.

No matter which point we choose, we get the same result in standard form.

Note:

Ax + By = C

x + 2y = 12

Here, A is 1, B is 2, and C is 12.

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