Parallel and Perpendicular Math Example 2

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Example 2

medium
Find the equation of the line through (4,1)(4, 1) that is perpendicular to 3x−y=63x - y = 6.

Solution

  1. 1
    Rewrite 3x−y=63x - y = 6 in slope-intercept form: y=3x−6y = 3x - 6. Slope is m1=3m_1 = 3.
  2. 2
    Perpendicular slope: m2=−1m1=−13m_2 = -\dfrac{1}{m_1} = -\dfrac{1}{3} (negative reciprocal).
  3. 3
    Use point-slope form through (4,1)(4,1): y−1=−13(x−4)y - 1 = -\dfrac{1}{3}(x - 4).
  4. 4
    Simplify: y=−13x+43+1=−13x+73y = -\dfrac{1}{3}x + \dfrac{4}{3} + 1 = -\dfrac{1}{3}x + \dfrac{7}{3}.

Answer

y=−13x+73y = -\dfrac{1}{3}x + \dfrac{7}{3}
Perpendicular lines have slopes that are negative reciprocals: their product equals −1-1. After finding the perpendicular slope, apply point-slope form to pass the new line through the required point.

About Parallel and Perpendicular

Parallel lines never intersect and have matching direction; perpendicular lines intersect at right angles.

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More Parallel and Perpendicular Examples

Example 1 easy

Find the equation of the line through [formula] that is parallel to [formula].

Example 3 easy

Are the lines [formula] and [formula] parallel, perpendicular, or neither?

Example 4 medium

Line [formula] passes through [formula] and [formula]. Find the equation of the line perpendicular t

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