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Slope of Parallel Lines
Slope of parallel lines are equal. The parallel lines are equally inclined with the positive xaxis and hence the slope of parallel lines are equal. If the slopes of two parallel lines are represented as m_{1}, m_{2} then we have m_{1} = m_{2}.
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 xaxis and the parallel lines are equally inclined with respect to the positive xaxis. If the slope of one line is m_{1} and the slope of another line is m_{2} and if it is given that both the lines are parallel, then we have m_{1} = m_{2}.
The equations representing parallel lines have equal coefficients for x and y. The line parallel to ax + by + c_{1} = 0, is ax + by + c_{2} = 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 m_{1} and m_{2}, 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.}
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Examples on Slope of Parallel Lines

Example 1: What is the slope of a line parallel to y = 2x + 3, and is passing through (1, 2)?
Solution:
The given equation of a line is y = 2x + 3. Comparing this with the slopeintercept form of the equation of line y = mx + c, we have m = 2
The required slope of the parallel line is equal to the slope of this given line and is equal to 2. Also, the given point (1, 2) is not required to find the slope of the parallel line.
Therefore the slope of the parallel line is m = 2.

Example 2: Find the equation of a line passing through (1, 2) and the slope of a parallel line is 2/3.
Solution:
The given slope of the parallel line is m = 2/3, and hence the slope of this required line is also m = 2/3.
The given point is \((x_1, y_1)\) = (1, 2)
The equation of a line can be calculated using point slope form of equation of a line.
\((y  y_1) = m(x  x_1)\)
\((y  2) = \frac{2}{3} (x  (1))\)
\(3(y  2) = 2(x + 1)\)
3y 6 = 2x + 2
2x  3y + 2 + 6 = 0
2x 3y + 8 = 0
Therefore the required equation of the line is 2x  3y + 8 = 0.
FAQs on Slope of Parallel Lines
What Is Slope of Parallel Lines in Maths?
The slope of parallel lines are equal. The parallel lines are equally inclined with respect to the positive xaxis and hence the slope of parallel lines are equal. If m_{1}, m_{2} are the slopes of parallel lines then we have m_{1} = m_{2}.
Where Do We Use the Slope of Parallel Lines?
The slope of parallel lines is useful to find the equation of the other parallel line. Also, the slope of parallel lines is helpful to find if both the lines are equally inclined with the positive xaxis.
What Are The Formulas For Slope of Parallel Lines?
The slopes of parallel lines are equal and the formula for the slope of parallel lines is m_{1} = m_{2}. The parallel lines are equally inclined with respect to the positive xaxis and hence the slope of parallel lines are equal.
How to Find Equation Of A Line From Slope Of Parallel Lines?
The equation of a line from the slope of parallel lines can be calculated using the pointslope form or the slopeintercept form. The slope of a line is equal to the slope of parallel lines, and we have m_{1} = m_{2}. And the equation of a parallel line can be calculated using the formulas \((y  y_1) = m(x  x_1)\), and y = mx + c.
What Is The Difference Between Slope of Parallel Lines And Slope of Perpendicular Lines?
The slope of parallel lines are equal in magnitude. The slope of perpendicular lines is such that the slope of one line is the negative inverse of the slope of another line. For two lines having slopes m_{1} and m_{2} the condition for the slope of parallel lines is m_{1} = m_{2} and the condition for the slope of perpendicular lines is m_{1}.m_{2} = 1.
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