Question 901779
The point of intersection is supposed to be x=20, and {{{5*20-4y=8}}},
{{{5*5-y=2}}}
{{{25-2=y}}}
{{{y=23}}}
The point (20,23).


The line perpendicular to that given line is {{{4x+5y=c}}}, which choice uses knowledge of the standard form in which the equation is written.  Substituting the found point of intersection (the expected point of intersection) will give the value for c:
{{{4*20+5*23=c}}}
{{{highlight_green(c=135)}}}.


Now, the line being found, perpendicular to the given line at (20,23) is
{{{4x+5y=135}}}.
Solve this for y, and THAT is your desired function, {{{g(x)}}}.


{{{5y=-4x+135}}}
{{{highlight(g(x)=y=-(4/5)x+27)}}}