Question 772657
Maybe easier as slope-intercept form.  "Gradient" must mean slope.


{{{by=-ax-c}}}
{{{y=-(a/b)x-c/b}}}
{{{2=3*5+v}}}  where v is the y-intercept to avoid confusion with the general form's variables.
{{{v=2-15}}}
{{{v=-13}}}

NOW back as slope intercept form, {{{y=3x-13}}}, and this can be put into the type of standard form originally asked for.

{{{y=3x-13}}}
{{{highlight(-3x+y+13=0)}}}  ________the ax+by+c=0 format
You can also multiply both sides by {{{-1}}}
{{{highlight(3x-y-13=0)}}}