What is the slope of a line that is perpendicular to a line whose equation is −2y=3x+7 ?

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What is the slope of a line that is perpendicular to a line whose equation is −2y=3x+7 ?

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Answer 1 · 2018-02-16T21:16:54

$\frac{2}{3}$ $2/3$

Explanation:

$given a line with slope m then the slope of a line$ $"given a line with slope m then the slope of a line"$
$perpendicular to it is$ $"perpendicular to it is"$

$m_{perpendicular} = - \frac{1}{m}$ $m_(color(red)"perpendicular")=-1/m$

$the equation of a line in point-slope form$ $"the equation of a line in "color(blue)"point-slope form"$ is.

$∙ x y = m x + b$ $•color(white)(x)y=mx+b$

$where m is the slope and b the y-intercept$ $"where m is the slope and b the y-intercept"$

$rearrange - 2 y = 3 x + 7 into this form$ $"rearrange "-2y=3x+7" into this form"$

$divide all terms by - 2$ $"divide all terms by "-2$

$\Rightarrow y = - \frac{3}{2} x - \frac{7}{2} \to with m = - \frac{3}{2}$ $rArry=-3/2x-7/2to"with "m=-3/2$

$\Rightarrow m_{perpendicular} = - \frac{1}{- \frac{3}{2}} = \frac{2}{3}$ $rArrm_(color(red)"perpendicular")=-1/(-3/2)=2/3$

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What is the slope of a line that is perpendicular to a line whose equation is −2y=3x+7 ?

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