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
Jim G.
Dec 11, 2017

#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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