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.
- Calculate distance between two points in space.

**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:

Various forms of equations of Straight Line

### Slope Point Format:

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

### Slope Intercept Format:

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,

Brigban, CC0, via Wikimedia Commons

**Angle between Two Lines**

Angle between two straight lines is given by:

**Distance Formula**

Distance between two points in the space \(P_1\) \((x_1,y_1,z_1)\) and \(P_2\) \((x_2,y_2,z_2)\) is given by:

This can be proved by repeated application of the Pythagorean Theorem.

Jim.belk, Public domain, via Wikimedia Commons