Question 1148569
<br>
Every line parallel to x+2y=12 will have an equation of the form x+2y=C for some constant C; every line perpendicular to x+2y=12 will have an equation of the form 2x-y=C for some constant C.  (Switch the two coefficients and make one of them negative; "1 and 2" becomes "2 and -1".)<br>
So the equation is of the form 2x-y=C, and the point (2,-4) is on the line.  So<br>
{{{2(2)-(-4) = C}}}
{{{4+4 = C}}}
{{{C = 8}}}<br>
So an equation of the line you are looking for is 2x-y = 8.<br>