Find the equation of the line with the given properties. Express the equation in general form or slope-intercept form. Perpendicular to the line -3x+y=13, contains the point (-6,-6). Can you give me a breakdown, so I can understand how to do this?

1 Answer
Jim G.
Jan 21, 2018

#y=-1/3x-8" and "x+3y-24=0#

Explanation:

#"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#

#"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 "-3x+y=13" into this form"#

#rArry=3x+13" with "m=3#

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

#rArry=-1/3x+b color(blue)" is the partial equation"#

#"to find b substitute "(-6,-6)" into the partial equation"#

#-6=2+brArrb=-6-2=-8#

#rArry=-1/3x-8larrcolor(red)" in slope-intercept form"#

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

#•color(white)(x)Ax+By+C=0#

#"where A is a positive integer and B, C are integers"#

#"rearrange "y=-1/3x-8" into this form"#

#"multiply all terms by 3"#

#rArr3y=-x-24#

#rArrx+3y-24=0larrcolor(red)"in general form"#

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