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 $3x-8y=8$?
- $2$
- $-\dfrac{8}{3}$
- $-\dfrac{8}{3}$
- $-\dfrac{3}{8}$
- $\dfrac{3}{8}$
Solution
- 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
$-8y=-3x+8$
- Divide all terms by $-8$
$y=\dfrac{3}{8} x -1$
- The slope of the given line is given by the coefficient of $x$ and is equal to $\dfrac{3}{8}$
- 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 $-1$)
$m \cdot \dfrac{3}{8}=-1$
- Solve for m
$m=-\dfrac{8}{3}$
Answer B
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