Question 532344
The equation for the line described is
{{{y=-4x-9}}}.
That equation is in the slope-intercept form, which looks like
{{{y=mx+b}}}, where {{{m}}} is the slope of the line and {{{b}}} is the y-coordinate for the point where the line intercepts the y-axis, called the y-intercept, or (sometimes) just intercept, for short.
That means that the slope of the line described is {{{m=-4}}}.
When lines are perpendicular, their slopes multiply to give you {{{-1}}},
meaning that the slope of the perpendicular line is
{{{m=(-1)/(-4)=1/4}}}
If that perpendicular line passes through the point (16,2) with
{{{x=16}}} and {{{y=2}}}, you have enough information to find the equation for that perpendicular line.
Knowing that it's going to be
{{{y=mx+b=(1/4)x+b}}}
you could substitute {{{x=16}}} and {{{y=2}}} to find {{{b}}}.
Otherwise, you could use the point-slope form of the equation, using the coordinates of the given point and the calculated slope to write the equation as
{{{y-2=(1/4)*(x-16)}}}.
A little algebra transforms the equation above into the slope-intercept form for the perpendicular line.