Question

Please help me understand this.

26. What positive value of k would make the lines below parallel in the (x, y) coordinate plane?
kx + 2y = 6
32x + ky = 18

F. 0
G. 3
H. 6
J. 8
K. 12

Thank you.

EDIT: Apart from substituting the numbers in, what's another method? This is to be treated as a timed test, so the fastest method possible is key.

Answer 1

for the lines to be parallel, the ration between the x and y terms must be the same

Answer 2

That I understand, but the variable k is confusing me so much

Answer 3

that therefore gives us that:\[\frac{32}{k}=\frac{k}{2}\]

Answer 4

make sense?

Answer 5

One sec, let me work this out on paper.

Answer 6

i.e. the second line is some multiple of the first line

Answer 7

Okay, so when I brought the terms over, I got...
kx + 2y = 6 becomes y = 3 - kx/2

y = 18/k - 32x/k

Answer 8

are you sure you have copied the question down correctly?

Answer 9

So I bring the slopes down...
-kx/2 = -32x/k
-64x = -k^2x
64 = k^2
8 = k

Answer 10

Yes. This is from an ACT practice test

Answer 11

OK - you have worked out the correct answer :)

Answer 12

I couldn't have done it without your assistance. Thank you!

Answer 13

yw :)