Question 965571

to find out which line is parallel to {{{x = y/3 - 8/3}}}, first write this one in slope-intercept form to find a slope

recall: parallel line have same slope

{{{x = y/3 - 8/3}}}.......both sides multiply by {{{3}}}

{{{3x = y - 8}}}....solve for {{{y}}}

{{{y=highlight(3)x+8 }}}=> a slope is {{{highlight(3)}}}

now write these equations one in slope-intercept form to find a slope

A. 
{{{2x + 3y = 4}}}
{{{3y =-2x+ 4}}}
{{{y =-(2/3)x+ 4/3}}} => a slope is {{{highlight(-2/3)}}}; so, this is NOT your answer

B. 

{{{-3x - 8y = 1}}}
{{{-3x - 1 =8y}}}
{{{-(3/8)x - 1/8 =y}}}=> a slope is {{{highlight(-3/8)}}}; so, this is NOT your answer


C. 

{{{6x - 2y = 5}}}
{{{6x - 5 = 2y}}}
{{{6x/2 - 5/2 = y}}}
{{{3x - 5/2 = y}}}=> a slope is {{{highlight(3)}}}; so, this IS your answer


D. 

{{{-8x + 6y = 6}}}
{{{6y =8x+ 6}}}
{{{y =8x/6+ 6/6}}}
{{{y =(4/3)x+ 1}}}> a slope is {{{highlight(4/3)}}}; so, this is NOT your answer

so, your answer is C.