# Find values of k if Parallel or if Perpendicular

• Jun 2nd 2010, 10:47 PM
larry21
Find values of k if Parallel or if Perpendicular
Find the values of $\displaystyle k$ for which the lines $\displaystyle kx-2y-1=0$ and $\displaystyle 8x-ky+3=0$ are parallel.

$\displaystyle \frac{k}{2}=\frac{8}{k}$

$\displaystyle {k^2}=16$

$\displaystyle k=\sqrt{16}=4$

But my textbook says it's plus or minus 4, I only got +4 why?

B.) Are there any values of $\displaystyle k$ that would make the two lines perpendicular? Explain.

How would I be able to find out?
• Jun 2nd 2010, 10:55 PM
undefined
Quote:

Originally Posted by larry21
Find the values of $\displaystyle k$ for which the lines $\displaystyle kx-2y-1=0$ and $\displaystyle 8x-ky+3=0$ are parallel.

$\displaystyle \frac{k}{2}=\frac{8}{k}$

$\displaystyle {k^2}=16$

$\displaystyle k=\sqrt{16}=4$

But my textbook says it's plus or minus 4, I only got +4 why?

B.) Are there any values of $\displaystyle k$ that would make the two lines perpendicular? Explain.

How would I be able to find out?

A)

The following is true

$\displaystyle x=4 \Longrightarrow x^2 = 16$

The following is not true

$\displaystyle x^2 = 16 \Longrightarrow x = 4$

That's because (-4)(-4) = 16.

B)

For perpendicular lines, either

1) one line is horizontal and the other is vertical, or

2) the slopes are negative reciprocals of each other.

So here we set

$\displaystyle \frac{k}{2}=-\frac{k}{8}$

You will get k = 0.