# General Equation of a Line

• Any equation of the form Ax + By + C = 0, with A and B are not zero, simultaneously, is called the general linear equation or general equation of a line.
• Slope-intercept form
→ If B ≠ 0, then Ax + By + C = 0 can be written as \tt y=-\frac{A}{B}x-\frac{C}{B}\Rightarrow y =mx+c
→ Here m (slope)=\tt -\frac{A}{B} and c (y-intercept)=\tt -\frac{C}{B}
→ If B = 0, then x = \tt -\frac{C}{A}, which is a vertical line whose slope is undefined and x-intercept is \tt -\frac{C}{A}.
• Intercept form
→ If C ≠ 0, then Ax + By + C = 0 can be written as \tt \frac{x}{-\frac{C}{A}}+\frac{y}{-\frac{C}{B}}=1\Rightarrow \frac{x}{a}+\frac{y}{b}=1
→ Here a (x-intercept)=\tt -\frac{C}{A} and b (y-intercept)=\tt -\frac{C}{B}
→ If C=0, then Ax + By + C = 0 can be written as Ax + By = 0, which is a line passing through the origin and, therefore, has zero intercepts on the axes.

### Part2: View the Topic in this video From 00:40 To 09:30

Disclaimer: Compete.etutor.co may from time to time provide links to third party Internet sites under their respective fair use policy and it may from time to time provide materials from such third parties on this website. These third party sites and any third party materials are provided for viewers convenience and for non-commercial educational purpose only. Compete does not operate or control in any respect any information, products or services available on these third party sites. Compete.etutor.co makes no representations whatsoever concerning the content of these sites and the fact that compete.etutor.co has provided a link to such sites is NOT an endorsement, authorization, sponsorship, or affiliation by compete.etutor.co with respect to such sites, its services, the products displayed, its owners, or its providers.

1. The slope intercept form of the equation Ax + By + C = 0 (B ≠ 0) is \tt y=-\frac{A}{B}x-\frac{C}{B}\Rightarrow y =mx+c

2. The Intercept form of the equation Ax + By + C = 0 (C ≠ 0) is \tt \frac{x}{-\frac{C}{A}}+\frac{y}{-\frac{C}{B}}=1\Rightarrow \frac{x}{a}+\frac{y}{b}=1

3. The normal form of the equation Ax + By + C = 0 is x cos ω + y sin ω = p