Question 461657
to find out which equation has a graph that is parallel to the graph of {{{4x - 2y = 1}}}, first write this equation in {{{slope-intercept}}} form:

{{{4x - 2y = 1}}}...->...{{{4x - 1 =2y}}}...->...{{{4x/2 - 1/2 =y}}}...->...{{{2x - 1/2 =y}}}

as you can see, the slope is {{{2}}} and a line with {{{same}}} slope will be {{{parallel}}} to this line; 

now write all your answer choices in {{{slope-intercept}}} form

a. {{{y = 2/3x - 2}}}  .......in {{{slope-intercept}}} form 

b. {{{2x - 4y = -1}}}

    {{{2x + 1 =4y}}}

{{{2x/4 + 1/4 =y}}}

{{{(1/2)x + 1/4 =y}}}...........in {{{slope-intercept}}} form

c. {{{6x -3y = 9 }}}

  {{{6x -9 = 3y }}}

{{{6x/3 -9/3 = y }}}

{{{2x -3 = y }}}.......in {{{slope-intercept}}} form


d. {{{y = -2x + 8}}}..............in {{{slope-intercept}}} form


so, a line with {{{same}}} slope as given line is {{{6x -3y = 9 }}}
 and your answer is {{{c}}}.


let's check it on a graph:

{{{ graph( 500, 500, -10, 10, -10, 10, 2x - 1/2, 2x -3) }}}