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

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) (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)

Start with the given equation

Subtract 2x from both sides

Simplify

Divide both sides by -3 to isolate y

Break up the fraction on the right hand side

Reduce and simplify

The original equation (standard form) is equivalent to (slope-intercept form)

The equation is in the form where is the slope and is the y intercept.

So this means the perpendicular slope is the negative reciprocal of . So the perpendicular slope is

Now let's look at

Start with the given equation

Add 6x to both sides

Divide both sides by B

Break up the fraction

So the slope of this equation is which is equal to (in order to be perpendicular to )

Set equal to

Multiply both sides by B

Multiply both sides by 2

Multiply

Divide both sides by -3

Simplify

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

Answer:

So our answer is

So B is equal to -4 in order to make perpendicular to

In other words, the equation is perpendicular to (notice I replaced B with -4)
Answer by Earlsdon(6294) (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:
Add 3y to both sides.
Subtract 8 from both sides.
Divide both sides by 3.
or
The slope is so the negative reciprocal is
The other equation is:
Add 6x to both sides.
Now divide both sides by B.
The slope here is and this is to equal
Multiply both sides by B.
Now multiply both sides by

Let;s graph the two resulting lines:

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