Question 879587
Get to know standard form for a line.
Ax+By=C can be solved for y and then the slope can be seen.  You will find that {{{-(A/B)}}} is the slope.  The slope of a line perpendicular would be the negative reciprocal of that, or  {{{(B/A)}}}.  What this means for the right hand member of standard form equation is either {{{-Bx+Ay}}}  or {{{Bx-Ay}}}.


The value of C will be different and depends on a point which the perpendicular line sought contains.  Substitute this point for x and y and compute C.

In your example, {{{1*x+3y=C}}}.
Substitute the given needed point:
{{{C=1*4+3*1}}}
{{{C=4+3}}}
{{{C=7}}}
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Equation x+3y=7 is perpendicular to 3x-y=6.