Question 999007
You must be looking for the values of A, B, and C.


{{{M=-A/B=7/1}}} and the given point lets you find C.


{{{-7x+1*y=-7*3+3}}}
{{{-7x+y=-18}}}
{{{highlight(7x-y=-18)}}}




A longer but easier way:
Solve the standard equation for y in terms of x and arrange into slope-intercept form.


{{{By=-Ax+C}}}
{{{y=-(A/B)x+C/B}}}
In this way, you see {{{M=-A/B=7/1}}} from which you can say  {{{A=-7}}} and {{{B=1}}}.


Now put this back into the standard form, left-hand member.
{{{-7x+1*y}}};
and remember, this was equated to C in that standard form equation.
{{{-7x+y=C}}}.
Having a known, given point on the line, you just substitute those coordinates to evaluate C.
-
{{{-7*3+3=C}}}
{{{C=-18}}} as found earlier.


Put everything back into the standard form equation.
{{{highlight(-7x+y=-18)}}}-----This seems to be better, and therefore a mistake must have happened in the earlier shown solution.