Question 214921
Any parallel line to {{{6x - 2y = 11}}} will be of the form {{{6x-2y=c}}} where 'c' is any real number. So all you need to do is plug in {{{x=1/3}}} and {{{y=0}}} into {{{6x-2y=c}}} to get {{{6(1/3)-2(0)=2-0=2=c}}} which would get you that {{{c=2}}}



So the equation parallel to {{{6x - 2y = 11}}} that goes through (1/3, 0) is {{{6x-2y=2}}}



Note: if you want the answer in slope-intercept form, simply solve for 'y' to get {{{y=3x-1}}}