Question 829514
Same slope, so {{{3x-5y=c}}}


Use the point.
{{{3(-1)-5(3)=c}}}
{{{c=-18}}}


Equation is {{{3x-5y=-18}}};
Solve for y and adjust to slope-intercept form, {{{y=mx+b}}}



SOME CONFUSION ABOUT THE 6 IN THE ORIGINAL EQUATION:


Try it this way.
Original equation, 3x-5y=6
{{{-5y=-3x+6}}}
{{{y=-(3/5)x-6/5}}}
Slope is {{{-(3/5)}}}.
For parallel line, you want the same slope, so you are looking for an equation, {{{y=-(3/5)x+b}}}, and you "do not yet know b".
Solving for b, obtain {{{b=y-(-3/5)x}}} and plug in the point to be contained:
{{{b=3-(-3/5)(-1)}}}
{{{b=3+(-3/5)=3-3/5=15/5-3/5=12/5}}};
Your wanted equation is then {{{highlight(y=-(3/5)x+12/5)}}}