How do you write the equation in slope intercept form perpendicular to the line 2x -3y = 12 and passes through the point (2, 6)?

Question

Eva Adamson · Accepted Answer

#y=-3/2x+9# #"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"#

Genesis Allen · Answer

undefined To find the equation of the line perpendicular to the given line 2x - 3y = 12 and passing through the point (2, 6), first, rearrange the given equation into slope-intercept form to find its slope. Then, determine the negative reciprocal of this slope to find the slope of the perpendicular line. Finally, use the point-slope form with the given point to write the equation of the perpendicular line in slope-intercept form.