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 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.

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