Question

Why is the answer B?

Answer 1

What you did with 4y/4=(-5x+12)/4 is to rewrite the original equation in point-slope form, and did not look for a new line. While this (same) line intersects the original line at (2,1/2), it intersects at ALL other points as well, so does not qualify as a good answer.

When two lines intersect at a single point, they must be not parallel to each other, much less identical. So you're looking at A, B or C. To check if the point (2, 1/2) lies on the line, substitute x=2 or y=1/2 in the equation and see if the other variable agrees.
Example, for B.
2y=3-x (substitute x=2) => 2y=3-2=1 => y=1/2, agrees with point where y=1/2. Since slope is (-1)/2=-1/2 ≠ -5/4, so B is a solution.
You will need to check the same way for A and C to find that the point (2,1/2) does not lie on either line, so they are not solutions.
Recall that D is eliminated because it is a line coincident with the given line.

Answer 2

Because it is the only equation that has a solution of (2, 1/2)

Plug in x = 2 and y = 1/2 into equation B and you will see that it works. It does not work for D.

Note that if the question was asking for an equation that is parallel to line l, then the answer would be D, but that was not what they were asking. So be careful answering some of the questions found on a math test. In other words, you got tricked.

"GGWP, NO RE"
- the test maker