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Standard Form Of The Equation Of A Line

This video explains how to convert functions from slope-intercept form, and point-slope form, to the standard form of the equation of a line.

The standard form of a line is written as:

Ax + By = C

where A, B, and C, are constants.

An example would be:

y = 3x + 7

Would be written as:

3x - y = -7
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Video-Lesson Transcript

The standard form of a line is

Ax + By = C

Where (x-term) + (y-term) = \#.

For example:

y = 3x + 7

Let’s solve to make this look like this (x-term) + (y-term) = \#

Let’s get all the terms on one side first by subtracting 3x on both sides

y = 3x + 7
-3x + y = 3x - 3x + 7
-3x + y = 7

It looks like it but we want the x term to be positive. So we divide both sides by -1

\dfrac{-3x}{-1} + \dfrac{y}{-1} = \dfrac{7}{-1}
3x - y = -7

Let’s solve another one

y - 5 = 2 (x + 7)
y - 5 = 2x + 14

Let’s bring all the variables to one side by subtracting y on both sides.

- 5 = 2x - y + 4

Then bring all the constant on one side by subtracting 4

- 5 - 4 = 2x - y + 4 - 4
- 9 = 2x - y

Let’s just rewrite it

2x - y = -9

Just to recap it’s just (x-term) + (y-term) = \#.

Standard Form of the Equation of a Line