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.
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
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 slope-intercept 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.
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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 x-axis and hence the slope of parallel lines are equal. If m1, m2 are the slopes of parallel lines then we have m1 = m2.
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 x-axis.
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 m1 = m2. The parallel lines are equally inclined with respect to the positive x-axis 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 point-slope form or the slope-intercept form. The slope of a line is equal to the slope of parallel lines, and we have m1 = m2. 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 m1 and m2 the condition for the slope of parallel lines is m1 = m2 and the condition for the slope of perpendicular lines is m1.m2 = -1.