# How do you find the slope that is perpendicular to the line 4x-2y=10?

Oct 2, 2016

${m}_{1} = 2 \mathmr{and} {m}_{2} = - \frac{1}{2}$

#### Explanation:

$4 x - 2 y = 10 \text{ } \leftarrow$ change into slope-intercept form

$4 x - 10 = 2 y \text{ } \div 2$

$2 x - 5 = y$

$y = 2 x - 5$

This is now in the form $y = m x + c$
It gives the slope and the y-intercept immediately

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Recall: Slopes which are perpendicular are negative reciprocals of each other. Their product is -1.

Here are some examples:

3/1xx-1/3 = -1;color(white)(x)-3/2xx2/3 = -1; color(white)(x) -4 xx1/4 = -1

In general if one slope is $\frac{a}{b}$, the other will be $- \frac{b}{a}$
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In $y = 2 x - 5 , \textcolor{w h i t e}{\times \times \times x} m = 2$

The slope perpendicular to 2 is$- \frac{1}{2}$

Note:
$- \frac{1}{2} = \frac{- 1}{2} = \frac{1}{-} 2 \text{ } \leftarrow$ the negative sign can be anywhere