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!