# How to Calculate Slope of Line – Slope of Parallel Lines

## How to Calculate Slope of Line

If given line makes an angle $$\theta$$ (0 $$\le$$ $$\theta$$ $$\le$$ 180 , $$\theta$$ $$\ne$$ 90) with positive direction of x-axis, then slope of line will be tan$$\theta$$ and is usually denoted by letter m.

i.e. m = tan$$\theta$$.

Slope of line Passing Through Two Points Formula

If A($$x_1,y_1$$) and B($$x_2,y_2$$) are the two points on a straight line & $$x_1$$ $$\ne$$ $$x_2$$ then the formula for slope of line passing through two points is

m = $$y_2-y_1\over {x_2-x_1}$$.

By using above formula, we can easily calculate the slope of line between two points.

Example : Find the slope of a line between the points A = (2, 0) and B = (4,6).

Solution : Here $$x_1, y_1$$ = (2, 0) and $$x_2, y_2$$ = (4, 6).

By using slope of line formula,

m = $$y_2-y_1\over {x_2-x_1}$$ = $$6-0\over 4-2$$

m = $$6\over 2$$

$$\implies$$ m = 3.

Hence slope of line is 3.

## Slope of Vertical Lines – Slope of Line Parallel to y-axis :

A vertical line is a line, parallel to y-axis and goes straight, up and down, in a coordinate plane.

In this case, $$\theta$$  = 90

m = tan$$\theta$$ = tan 90 = $$\infty$$

i.e. m does not exist when the slope of line is parallel to y-axis.

## Slope of Horizontal Lines – Slope of Line Parallel to x-axis :

A horizontal line which is parallel to x-axis and goes straight, left and right in the coordinate plane.

In this case, $$\theta$$  = 0

m = tan$$\theta$$ = tan 0 = 0

i.e. m = 0

## Slope of Parallel Lines :

Let $$m_1$$ and $$m_2$$ be slopes of two given lines,

then, $$m_1$$ = $$m_2$$

## Slope of Perpendicular Lines :

Let $$m_1$$ and $$m_2$$ be slopes of two given lines,

then, $$m_1$$ $$\times$$ $$m_2$$ = -1

## Slope of Line Equation :

The slope of line equation is also called equation of line in slope form and is  written as

y = mx + c.

where m is the slope of line and c is the intercept on y-axis.

Example : Find the slope of a line whose equation is y = 3x + 4.

Solution : Given equation is y = 3x + 4

Comparing it with slope of line equation, y = mx + c

we get, m = 3.

Hope you learnt how to calculate slope of line, learn more concepts of straight lines and practice more questions to get ahead in the competition. Good luck!