Which equation represents a line that is parallel to the line whose equation is 2x+3y=12?

Question

The choices are:

6y-4x=2
6y=4x=2
4x-6y=2
6x=4y=-2

Please explain your answer if you can.

Sorry, I meant:
6x=4y-2

Answer 1

A parallel line has the same slope.

Put your equation in y=mx+b form:
2x+3y=12 (subtract 2x from both sides)
3y = -2x +12 (divide both sides by 3)
y = -(2/3)x +4
So, your slope (m) is -2/3

Now, check the other equations for which one has a slope of -2/3

6y-4x=2 has m=(2/3)
6y=4x=2
(okay this is not an equation, i'll assume you meant 6y+4x=2, which has a slope m of -2/3)
4x-6y=2 has m=2/3
6x=4y=-2 (okay this is not an equation, i'll assume you meant 6x+4y=-2, which has a slope m of -3/2

So your answer would be 6y+4x=2 (if that is what that says)

Answer 2

Actually none...suppose you have two lines with the following formula : ax+by = c and mx+ny = d
for these lines to be parallel, the lines should have equal slopes that is b/a = n/y (of course you should rearrange the formula to be like ax + by = c, that is put x & y on the left side both or right side)...
2x+3y=12 --> m(slope) = 3/2
6y-4x=2 ---> m = -6/4 = -3/2
6y=4x=2 ---> 6y = 2 ---> y = 3 ..&.. 4x = 2 ---> x = 2 (it;s not a line, it's a single point)
4x-6y=2 ---> m = -6/4 = -3/2
6x=4y=-2 ---> it isn't a line as well, it's just a point

Good Luck

Answer 3

rewriting equation into standard format:
y = mx + b
where:
m=slope
b=y-intercept

2x+3y=12
3y = -2x + 12
y = -2/3x + 4

So, now we know the "slope" is -2/3.
Now we simply select the answer with the same slope:
It has to have something with:
6y+4x=2

Because then when we rewrite it to the standard eq we get:
6y = -4x + 2
y = -2/3(x) + 1/3