# 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"#