# Thread: Find Value of k

1. ## Find Value of k

Find the value of $\displaystyle k$ if the lines $\displaystyle 3x-2y-5=0$ and $\displaystyle kx-6y+1=0$ are parallel.

$\displaystyle 3x-2y-5=0$

$\displaystyle 3x-5=2y$

$\displaystyle \frac{3}{2}x-\frac{5}{2}=y$

$\displaystyle m=\frac{3}{2}$

I found the slope of the parallel lines but have no idea how I would find $\displaystyle k$
Can anyone help please? Thank you very much!

2. Originally Posted by larry21
Find the value of $\displaystyle k$ if the lines $\displaystyle 3x-2y-5=0$ and $\displaystyle kx-6y+1=0$ are parallel.

$\displaystyle 3x-2y-5=0$

$\displaystyle 3x-5=2y$

$\displaystyle \frac{3}{2}x-\frac{5}{2}=y$

$\displaystyle m=\frac{3}{2}$

I found the slope of the parallel lines but have no idea how I would find $\displaystyle k$
Can anyone help please? Thank you very much!
Maybe from observing what you just did you can see that for the line

Ax + By + C = 0

the slope (assuming it's defined) is -A/B

But you don't have to see this, you can just solve the second equation for y (thus putting it into slope-intercept form), see what the slope is (it will be in terms of k) and then set that to 3/2.

3. So.....

$\displaystyle \frac{kx}{6}+\frac{1}{6}=y$

I don't get how this helps me?

4. Originally Posted by larry21
So.....

$\displaystyle \frac{kx}{6}+\frac{1}{6}=y$

I don't get how this helps me?
The lines are parallel, meaning they have the same slope. Write

$\displaystyle \frac{3}{2}=\frac{k}{6}$ and solve for $\displaystyle k$.