Question 102866
Er...not quite, athough you are on the right track!
Start with the fact that perpendicular lines have slopes that are the negative reciprocal of each other.
You have:
{{{2x-3y = 8}}} Add 3y to both sides.
{{{2x = 3y+8}}} Subtract 8 from both sides.
{{{2x-8 = 3y}}} Divide both sides by 3.
{{{(2/3)x-8/3 = y}}} or
{{{y = (2/3)x-8/3}}} The slope is {{{2/3}}} so the negative reciprocal is {{{-3/2}}}
The other equation is:
{{{-6x+By = 3}}} Add 6x to both sides.
{{{By = 6x+3}}} Now divide both sides by B.
{{{y = (6/B)x+3/B}}} The slope here is {{{6/B}}} and this is to equal {{{-3/2}}}
{{{6/B = -3/2}}} Multiply both sides by B.
{{{6 = -(3/2)B}}} Now multiply both sides by {{{-2/3}}}
{{{(-2/3)*6 = B}}}
{{{B = -4}}}
Let;s graph the two resulting lines:
{{{graph(400,400,-5,5,-5,5,(2/3)x-8/3,(-3/2)x-3/4)}}}