Question

Why is the answer B? Plz explain.

Answer 1

For line l to intersect line m at point (2, 1/2), line m must have the point (2,1/2) on its graph. It is implied that line l already has the point (2, 1/2). If line m does not have it, then there will be no intersection at that specific point.

Try checking every choice to see if it has point (2,1/2) on the graph.
Note that (x,y) = (2,1/2); check by using x=2 and y=1/2.

For A,

   2x = y/2
   2(2) = (1/2) / 2
   4 ≠ 1/4

Cannot be choice A as it results in a false equation; this choice will not go through (2,1/2)

For B:

   2y = 3 - x
   2(1/2) =  3 - 2
   1 = 1

This is a true equation so the point (2,1/2) is on the graph of 2y=3-x. This means that if this is the equation for line m, then line m will have a point at (2,1/2) and therefore intersect with line l. Therefore, B is the answer.

The rest of the choices are false as shown:

For C:
 
   2x + 4y = 8
   2(2) + 4(1/2) = 8
   4 + 2 = 8
   6 ≠ 8

Cannot be choice C as it results in a false equation; this choice will not go through (2,1/2)

For D:

   y = 4 - (5/4)x
   1/2 = 4 - (5/4)(2)
   1/2 = 4 - 5/2
   1/2 = 8/2 - 5/2
   1/2≠ 3/2

Cannot be choice D as it results in a false equation; this choice will not go through (2,1/2)