Question 682834
Any line that is parallel to 2x-3y=1 is the equation 2x-3y=C where C is any real number (but 1)


2x-3y=C


2(3)-3(0)=C ... Plug in (3,0) which is the point the parallel line goes through.


6-0=C


6=C


C = 6


So the equation of the parallel line in standard form is 2x - 3y = 6



If you want the equation in slope intercept form, then


{{{2x - 3y = 6}}}


{{{-3y = -2x + 6}}}


{{{y = (-2x)/(-3) + 6/(-3)}}}


{{{y = expr(2/3)x-2}}}


So the equation of the parallel line in slope-intercept form is {{{y = expr(2/3)x-2}}}