How do you write the equation in slope intercept form perpendicular to the line 2x -3y = 12 and passes through the point (2, 6)?
1 Answer
Apr 26, 2018
Explanation:
#"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-3y=12" into this form"#
#"subtract 2x from both sides"#
#rArr-3y=-2x+12#
#"divide all terms by "-3#
#rArry=2/3x-4larrcolor(blue)"in standard form"#
#"with "m=2/3#
#"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_("perpendicular")=-1/(2/3)=-3/2#
#rArry=-3/2x+blarrcolor(blue)"is the partial equation"#
#"to find b substitute "(2,6)" into the partial equation"#
#6=-3+brArrb=6+3=9#
#rArry=-3/2x+9larrcolor(red)"equation of perpendicular line"#