Question 893292
Given 4y=x-4, slope-intercept form is {{{y=x/4-1}}}.  Slope is {{{(1/4)}}}.


A line perpendicular to that must be like {{{y=-4x+b}}}, but you do not yet know b.
You want this perpendicular line to contain the point, (2,6).


{{{y=-4x+b}}}
{{{y+4x=-4x+b+4x}}}
{{{y+4x=b}}}
{{{b=y+4x}}}
substitute the point.
{{{b=6+4*2}}}
{{{highlight_green(b=14)}}}


Line's equation you want is {{{highlight(y=-4x+14)}}}.