Question 892519
{{{2x+6y=24}}}, the given equation.
Solve for y.
{{{6y=-2x+24}}}
{{{y=-(1/3)x+4}}}
Slope is {{{-1/3}}}.  Any line in the plane perpendicular to it must have slope negative reciprocal of this value; meaning that the line you are looking for must have slope 3.


Wanting the line you are looking for to contain point (2,1), then use slope intercept form for the line you want, solved for b.

{{{y=3x+b}}}  -------- you want to know what b is, so solve for it, and then substitute the point which is supposed to be on the line you want.
{{{y-3x=b}}}
{{{b=y-3x}}}
{{{b=1-3*2}}}
{{{b=-5}}}-------the y-intercept.


Line you want is {{{highlight(y=3x-5)}}}.