Question

HELP ATTACHED IMAGE

Answer 1

#2 is correct. You know this because when you solve for y, the x's have the same slope.

Answer 2

Only 2. I agree.

Answer 3

y=mx+b where "m" is the gradient <-- marmar i hope you are familiar with this equation.
so for 2y =2-2x, you agree that it can be written as 2y=-2x+2, and after you factorise/simplify(ie divide everything by 2) it will look like
y =-x+1
does this look familiar to the form y= mx+b, hence we may deduce that m= -1

if we then look at the options they offer for the SECOND one 1x -4 =-1y
do you agree that this is the same as writing 1y= -1x +4
thus "m" =-1 which is the SAME for 2y =2-2x

for the THIRD one, 2y -4 =x, you agree this is the same as
y =(x/2)+(4/2) where "m" = 1/2 which is NOT THE SAME for
2y =2-2x

for the FOURTH one, 2y -3 =2x, you agree this is the same as writing y=(2x/2) +(3/2), thus "m" =1 which is NOT THE SAME for 2y =2-2x

therefore, it is true for only the SECOND ONE. and because it is true for the SECOND ONE we may dismiss the FIRST ONE which is "None of them" as a possible answer.

so the final answer is the SECOND ONE.

i hope this makes sense

Answer 4

http://www.wolframalpha.com/input/?i=2x%2B2y%3D2+and+x-4%3D-y+and+2x%3Dy%2B4+and+2y-4%3Dx+and+2y-3%3D2x

Here's a (hopefully) easy visualization of the problem.

Answer 5

nice diagram!