Slope Of Parallel - Definition, Formula, Derivation, Examples

Slope of Parallel Lines

Slope of parallel lines are equal. The parallel lines are equally inclined with the positive x-axis and hence the slope of parallel lines are equal. If the slopes of two parallel lines are represented as m1, m2 then we have m1 = m2.

Let us learn more about the slope of parallel lines, their derivation, with the help of examples, FAQs.

1.	What Is the Slope of Parallel Lines?
2.	Derivation of Slope of Parallel Lines
3.	Examples on Slope of Parallel Lines
4.	Practice Questions
5.	FAQs on Slope of Parallel Lines

What is the Slope of Parallel Lines?

Slopes of parallel lines are equal. The slope of a line is computed with respect to the positive x-axis and the parallel lines are equally inclined with respect to the positive x-axis. If the slope of one line is m1 and the slope of another line is m2 and if it is given that both the lines are parallel, then we have m1 = m2.

The equations representing parallel lines have equal coefficients for x and y. The line parallel to ax + by + c1 = 0, is ax + by + c2 = 0. On observation, we find that the coefficients of x ad y in both the equations are equal.

Derivation of Slope of Parallel Lines

The condition for slope of the parallel lines can be derived from the formula of the angle between two lines. The angle between two parallel lines is 0º or 180º. For two lines having slopes m1 and m2, the angle between the two lines can be calculated using Tanθ.

\(Tanθ = \dfrac{m_1 - m_2}{1 + m_1.m_2}\)

The angle between two parallel lines is 0º, and we have Tan0º = Tan180º = 0.

\(Tan0º = \dfrac{m_1 - m_2}{1 + m_1.m_2}\)

\(0 = \dfrac{m_1 - m_2}{1 + m_1.m_2}\)

\(0 = m_1 - m_2\)

\( m_1 - m_2 = 0\)

\( m_1 = m_2\)

Thus the slope of two parallel lines is equal in magnitude.

☛Related Topics

• Slope Intercept Form
• Point Slope Form
• Coordinate Geometry
• Cartesian Coordinate System