1. ## lines in xy

I can't believe I'm having so much trouble

#1:

For which values of k are the following pairs of lines parallel? perpendicular?
3x+4y=9
x+ky=6

#2:

(k-1)y+(k+1)x+k-1=0 (k is a constant)
For what value of k is the graph of this function parallel to the x-axis?

I tried re-arranging it, but it confused me even more.

2. Originally Posted by starship
I can't believe I'm having so much trouble

#1:

For which values of k are the following pairs of lines parallel? perpendicular?
3x+4y=9
x+ky=6

...
Two lines $\displaystyle l_1$ and $\displaystyle l_2$ are parallel if their slopes are equal.

Two lines $\displaystyle l_1$ and $\displaystyle l_2$ are perpendicular if the product of their slopes equals (-1).

$\displaystyle l_1: 3x+4y = 9~\implies~y = -\frac34 x + \frac94$

$\displaystyle l_2: x+ ky = 6~\implies~ y = -\frac1k x + \frac6k$

$\displaystyle l_1 \parallel l_2: -\frac34 = -\frac1k$ Solve for k

$\displaystyle l_1 \bot l_2: \left(-\frac34\right) \cdot \left(-\frac1k\right) = -1$ . Solve for k

3. Originally Posted by starship
...
#2:

(k-1)y+(k+1)x+k-1=0 (k is a constant)
For what value of k is the graph of this function parallel to the x-axis?

...
A line with the equation $\displaystyle y = a~,~a \in \mathbb{R}$ is a parallel to the x-axis that means the coefficient of x must be zero:

$\displaystyle (k-1)y+(k+1)x+k-1=0$ that means: $\displaystyle k+1=0~\iff~ k = -1$