How do you find the general form of the line that passes through A(3, -4); perpendicular to the line 2x - 6y = 11?

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How do you find the general form of the line that passes through A(3, -4); perpendicular to the line 2x - 6y = 11?

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Answer 1 · 2017-12-11T11:29:37

$3x+y-5=0$

Explanation:

$"the equation of a line in "color(blue)"general form"$ is.

$color(red)(bar(ul(|color(white)(2/2)color(black)(Ax+By+C=0)color(white)(2/2)|)))$

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

$•color(white)(x)y=mx+b$

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

$"rearrange "2x-6y=11" into this form"$

$rArr6y=2x-11$

$rArry=1/3x-11/6larrcolor(red)"in slope-intercept form"$

$rArr"slope "=m=1/3$

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

$•color(white)(x)m_(color(red)"perpendicular")=-1/m$

$rArrm_(color(red)"perpendicular")=-1/(1/3)=-3$

$rArry=-3x+b color(blue)" is the partial equation"$

$"to find b substitute "(3,-4)" into the partial equation"$

$-4=-9+brArrb=5$

$rArry=-3x+5larrcolor(red)"in slope-intercept form"$

$rArr3x+y-5=0larrcolor(red)"in general form"$

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How do you find the general form of the line that passes through A(3, -4); perpendicular to the line 2x - 6y = 11?

1 Answer

Explanation:

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