## Straight Lines

# 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 A*x*+ B*y*+ C = 0 can be written as A*x*+ B*y*= 0, which is a line passing through the origin and, therefore, has zero intercepts on the axes.

### Part1: View the Topic in this video From 50:01 To 54:54

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

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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