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 positiveslope of line 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!

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