For what value of k are the lines 2x+3y=4k and x-2ky=7 parallel? I really have no idea how to deal with the extra variable.

Question

directrix · Answer

Something to remember: 

Parallel lines have the same slope.

directrix · Answer

2x + 3y = 4k
3y = -2x + 4k
y = (-2/3)x + (4/3)k
Slope is -2/3

directrix · Answer

Will you find the slope of this line?

x-2ky=7


@CasidyCat

anonymous · Answer

@Directrix That was the problem. I couldn't find the slope for the second equation.

directrix · Answer

x - 2ky = 7
2ky = x - 7
y = (1/(2k))x - (7/(2k))
Slope is 1/(2k)

directrix · Answer

If the lines are parallel, the slopes are equal:
1/(2k) = -2/3
2k = -3/2
4k = -3
k = -3/4
k = -0.75

directrix · Answer

Input from @jeff1949

directrix · Answer

@CasidyCat    Any questions?

anonymous · Answer

Nope, thank you! I was just getting confused as to what I should consider the k, but I understand now.

directrix · Answer

Alrighty, then.