Question 102866
*[invoke converting_linear_equations "standard_to_slope-intercept", 2, -3, 8, 2, 1]


So this means the perpendicular slope is the negative reciprocal of {{{2/3}}}. So the perpendicular slope is {{{-3/2}}}



Now let's look at {{{-6x +By = 3}}}


{{{-6x+By=3}}} Start with the given equation




{{{By=3+6x}}}Add 6x to both sides



{{{y=(3+6x)/B}}} Divide both sides by B



{{{y=3/B+(6/B)x}}}Break up the fraction



So the slope of this equation is {{{6/B}}} which is equal to {{{-3/2}}} (in order to be perpendicular to {{{2x-3y=8}}})



{{{6/B=-3/2}}} Set {{{6/B}}} equal to {{{3/2}}}



{{{6=(-3/2)*B}}} Multiply both sides by B


{{{6*2=-3*B}}} Multiply both sides by 2


{{{12=-3*B}}} Multiply


{{{12/-3=B}}} Divide both sides by -3



{{{-4=B}}} Simplify




------------------------------------


Answer:


So our answer is  {{{B=-4}}} 


So B is equal to -4 in order to make {{{-6x +By = 3}}} perpendicular to {{{2x-3y=8}}}



In other words, the equation  {{{-6x -4y = 3}}} is perpendicular to {{{2x-3y=8}}} (notice I replaced B with -4)