Question

Please answer & explain this

Answer 1

Parallel lines have the same slope.

To compare the slopes of two different lines, you have to get
both equations into the form of    
                                                        y = 'm' x  +  (a number) .

In that form, the 'm' is the slope of the line.
Notice that it's the number next to the 'x' .

The equation given in the question is    y = 3 - 2 x .
Right away, they've done something to confuse you.
You always expect the 'x' term to be right after the 'equals' sign,
but here, they put it at the end.  The slope of this line is the  -2 .

Go through the choices, one at a time.
Look for another one with a slope of  -2 .
Remember, rearrange the equation to read ' y = everything else ',
and then the slope is the number next to the 'x'.

Choice #4:  y = 4x - 2 .  The slope is  4 .  That's not it.

Choice #3:  y = 3 - 4x .  The slope is  -4 .  That's not it.

Choice #2).                       2x + 4y = 1

Subtract 2x from each side:    4y = 1 - 2x

Divide each side by  4 :             y = 1/4  -  1/2 x .

                                                     The slope is  -1/2.  That's not it.

Choice #1).                                 4x + 2y = 5

Subtract 4x from each side:              2y = 5 - 4x

Divide each side by 2 :                        y = 5/2  - 2 x .

                                                       The slope is -2 .
                                                       This one is it.  
                This one is parallel to  y = 3 - 2x ,
                 because they have the same slope.