** Straight Line **

##### Straight Line Important Formulae

**After successful completion of this topic, you should be able to:**

- Find and interpret equation of a straight line in various forms.
- Perform slope calculations including parallel and perpendicular lines.
- Find angle between two coplanar, non-parallel lines.

#### Slope of a Straight Line

##### Slope of a Straight Line

**Slope** of a straight line gives you an idea about its inclination with reference to x-axis. Slope is also referred as **gradient**.

#### Equation of a Straight Line

The equation of a straight line (or any curve) is the relation between the x and y (and z) coordinates of all points lying on it.

The general form of the equation of a straight line is: \[Ax + By + C = 0\]

**Slope Point Format:**

\[y - y_{1} = m (x - x_{1})\]

where \(x_{1}\) and \(y_{1}\) are the coordinates of the point through which the line passes.

**Slope Intercept Format:**

\[y = mx + b\]

where m = slope and b = y-intercept

For the above line, y-intercept = 1, and

slope = \(\dfrac{\mathrm{Rise}}{\mathrm{Run}}\) = \(\dfrac{2}{4}\) = \(\dfrac{1}{2}\)

So the equation will be, \[y = 0.5x + 1\] \[2y = x + 2\] \[x - 2y + 2 = 0\]

**Double Intercept Format:**

\[\dfrac{x}{a}+\dfrac{y}{b} = 1\]

where a = x intercept and b = y intercept

#### Parallel and Perpendicular Lines

For parallel lines slopes are equal i.e. \(m_{1} = m_{2}\)

For perpendicular lines

\(m_{1} * m_{2}\) = -1

or,
\[m_2 = \dfrac{-1}{m_1}\]

Brigban, CC0, via Wikimedia Commons

#### Angle between Two Lines

Angle between two straight lines is given by: \[\alpha = \tan^{-1}\left(\dfrac{m_{2}-m_{1}}{1+ m_{1}m_{2}}\right)\]