Find Slope of Perpendicular Line

Find the slope of a line perpendicular to a given line

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Example 1

Example on how to find the slope of a line perpendicular to a given line.

What is the slope of the line perpendicular to the line with equation $3x-8y=8$?

  1. $2$

  2. $-\dfrac{8}{3}$

  3. $-\dfrac{8}{3}$

  4. $-\dfrac{3}{8}$

  5. $\dfrac{3}{8}$

Solution


  1. In order to find the slope of a line given its equation, we need to rewrite the given equation in slope intercept form by solving for $y$. The given equation maybe written as

    $-8y=-3x+8$

  2. Divide all terms by $-8$

    $y=\dfrac{3}{8} x -1$

  3. The slope of the given line is given by the coefficient of $x$ and is equal to $\dfrac{3}{8}$

  4. The slope $m$ of the line perpendicular to the given line is found by solving the equation (the product of the slopes of two perpendicular lines is equal to $-1$)

    $m \cdot \dfrac{3}{8}=-1$

  5. Solve for m

    $m=-\dfrac{8}{3}$

    Answer B
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