SOLUTION: Find B so that -6x +By = 3 is perpendicular to 2x-3y=8. I took simplified y=-2/3x - 8/3 and y=6x + 3/B. any number for B must be positive in order for the lines to be perpe

Algebra ->  Linear-equations -> SOLUTION: Find B so that -6x +By = 3 is perpendicular to 2x-3y=8. I took simplified y=-2/3x - 8/3 and y=6x + 3/B. any number for B must be positive in order for the lines to be perpe      Log On


   

Question 102866This question is from textbook Intermediate Algebra
: Find B so that -6x +By = 3 is perpendicular to 2x-3y=8.
I took simplified y=-2/3x - 8/3 and y=6x + 3/B.
any number for B must be positive in order for the lines to be perpendicular.
is this correct? This question is from textbook Intermediate Algebra

Found 2 solutions by jim_thompson5910, Earlsdon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)
Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)


2x-3y=8 Start with the given equation


2x-3y-2x=8-2x Subtract 2x from both sides


-3y=-2x%2B8 Simplify


%28-3y%29%2F%28-3%29=%28-2x%2B8%29%2F%28-3%29 Divide both sides by -3 to isolate y


y+=+%28-2x%29%2F%28-3%29%2B%288%29%2F%28-3%29 Break up the fraction on the right hand side


y+=+%282%2F3%29x-8%2F3 Reduce and simplify


The original equation 2x-3y=8 (standard form) is equivalent to y+=+%282%2F3%29x-8%2F3 (slope-intercept form)


The equation y+=+%282%2F3%29x-8%2F3 is in the form y=mx%2Bb where m=2%2F3 is the slope and b=-8%2F3 is the y intercept.





So this means the perpendicular slope is the negative reciprocal of 2%2F3. So the perpendicular slope is -3%2F2


Now let's look at -6x+%2BBy+=+3

-6x%2BBy=3 Start with the given equation



By=3%2B6xAdd 6x to both sides


y=%283%2B6x%29%2FB Divide both sides by B


y=3%2FB%2B%286%2FB%29xBreak up the fraction


So the slope of this equation is 6%2FB which is equal to -3%2F2 (in order to be perpendicular to 2x-3y=8)


6%2FB=-3%2F2 Set 6%2FB equal to 3%2F2


6=%28-3%2F2%29%2AB Multiply both sides by B

6%2A2=-3%2AB Multiply both sides by 2

12=-3%2AB Multiply

12%2F-3=B Divide both sides by -3


-4=B Simplify



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Answer:

So our answer is B=-4

So B is equal to -4 in order to make -6x+%2BBy+=+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)

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
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%2B8 Subtract 8 from both sides.
2x-8+=+3y Divide both sides by 3.
%282%2F3%29x-8%2F3+=+y or
y+=+%282%2F3%29x-8%2F3 The slope is 2%2F3 so the negative reciprocal is -3%2F2
The other equation is:
-6x%2BBy+=+3 Add 6x to both sides.
By+=+6x%2B3 Now divide both sides by B.
y+=+%286%2FB%29x%2B3%2FB The slope here is 6%2FB and this is to equal -3%2F2
6%2FB+=+-3%2F2 Multiply both sides by B.
6+=+-%283%2F2%29B Now multiply both sides by -2%2F3
%28-2%2F3%29%2A6+=+B
B+=+-4
Let;s graph the two resulting lines:
graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C%282%2F3%29x-8%2F3%2C%28-3%2F2%29x-3%2F4%29