## Straight Lines

# Various Forms of the Equation of a Line

- Equation of horizontal line passing through (x
_{1 }y_{1}) is y = y_{1} - Equation of vertical line passing through (x
_{1 }y_{1}) is x = x_{1} - The equation of the line whose slope is ‘m’ and which cuts an intercept ‘c’ on the y-axis is y = mx + c
- The equation of the line whose slope is ‘m’ and which cuts an intercept ‘a’ on the x - axis is y = m(x – a)
- The equation of a straight line having x – intercept ‘a’ and ‘y’ intercept ‘b’ is \tt \frac{x}{a}+\frac{y}{b}=1 (a, b ≠0)
- The equation of the line with slope ‘m’ and passing through the point (x
_{1 }y_{1}) is y – y_{1}= m (x_{1 }y_{1}) - The equation of a line passing through ‘2’ points (x
_{1 }y_{1}) and (x_{2}y_{2}) is (y – y_{1}) (x_{2}– x_{1}) = (y_{2}– y_{1}) (x – x_{1}) - The equation of the straight line upon which the length of the normal drawn from origin is ‘P’ and this perpendicular makes an angle ‘∝’ , (0 ≤ ∝ < 2π) with positive x–axis is x cos ∝ + y sin ∝ = P (P > 0)

### View the Topic in this video From 21:22 To 50:00

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1. Equation of the horizontal line having distance a from the x-axis is either y = a or y = −a.

2. Equation of the vertical line having distance b from the y-axis is either x = b or x = −b.

3. The point (x, y) lies on the line with slope m and through the fixed point (x_{0}, y_{0}), if and only if its coordinates satisfy the equation y − y_{0} = m (x − x_{0}).

4. Equation of the line passing through the points (x_{1}, y_{1}) and (x_{2}, y_{2}) is given by \tt y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\left(x-x_{1}\right).

5. The point (x, y) on the line with slope m and y-intercept c lies on the line if and only if y = mx + c.

6. If a line with slope m makes x-intercept d. Then equation of the line is y = m (x − d).

7. Equation of a line making intercepts a and b on the x-and y-axis, respectively, is \tt \frac{x}{a}+\frac{y}{b}=1.

8. The equation of the line having normal distance from origin p and angle between normal and the positive x-axis ω is given by x cos ω + y sin ω = p

9. The equation of the straight line passing through (x_{1 }y_{1}) and makes an angle ‘θ’ with the positive direction of x – axis is \tt \frac{x-x_{1}}{\cos \theta}+\frac{y-y_{1}}{\sin \theta}