General Form of Equation of a Line
The "General Form" of the equation of a straight line is:
Ax + By + C = 0
A or B can be zero, but not both at the same time.
The General Form is not always the most useful form, and you may prefer to use:
The Slope-Intercept Form of the equation of a straight line: y = mx + b |
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or |
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The Point-Slope Form of the equation of a straight line: y - y1 = m(x - x1) |
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Example: Convert 4x - 2y - 5 = 0 to Slope-Intercept Form
We are heading for
y = mx + b
| Start with | 4x - 2y - 5 = 0 | |
| Move all except y to the left: | -2y = -4x + 5 | |
| Divide all by (-2): | y = 2x - 5/2 | |
And we are done! (Note: m=2 and b=-5/2)
Why Use It?
It has the advantage of working well with vertical lines, which the Slope-Intercept Form and Point-Slope Form do not.