### General form for the equation of a line: *0 = Ax + By + C*

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The formula ** 0 = Ax + By + C** is said to be the

At first it is difficult to imagine the slant and position of the line just by looking at the general form. However, we can change the general form into slope-intercept form and then get a good idea of what we are looking at. Here's the algebra:

0 = Ax + By + C |
Starting equation |

0 - By = Ax + By -By + C |
Subtract from each sideBy |

-By = Ax + C |
Left side: 0 - By = -ByRight side: By - By = 0 |

-By/-B = Ax/-B + C/-B |
Divide each side by -B |

y = (-A/B)x + (-C/B) |
Left side: -By/-B = yRight side: Ax/-B = (-A/B)xRight side: C/-B = (-C/B) |

y = mx + b |
Where: m = (-A/B)Where:
b = (-C/B) |

As the previous algebra has shown, if we start with this general form:

*0 = Ax + By + C*

Then the slope of the line is:

*slope = m = -A/B*

And the y-intercept is:

*y-intercept = b = -C/B*

Let's start with this general form:

*0 = Ax + By + C*

Let:

*A = 2, B = 3, C = 4*

So:

*0 = 2x + 3y + 4*

** slope = m = -A/B = -2/3 = -0.67** (approximately)

** y-intercept = b = -C/B = -4/3 = -1.33** (approximately)

Our line in slope-intercept form:

*y = mx + b*

** y = -0.67x + (-1.33)** or

Below is a graph that presents a line as it is given by the general form
equation. You can control the example values for ** A**,

This is an EZ Math Movie. Click the 'Show system' checkbox to expose the EZ Math Movie language. You do not need to understand EZ Math Movie to use this application.

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