The proper perpendicular slope should be -1/4 instead of positive 1/4. The y intercept is also incorrect
Let's call the y intercept b for now
m = -1/4 is the perpendicular slope
(x,y) = (16,1) is the point the perpendicular line goes through
breaking this down further means x = 16 and y = 1 pair up together
y = mx+b
y = (-1/4)*x+b ... replace m with -1/4
y = (-1/4)*16+b .... replace x with 16
1 = (-1/4)*16+b .... replace y with 1
1 = -4+b ... multiply -1/4 and 16 to get -4
1+4 = -4+b+4 ... add 4 to both sides
5 = b
b = 5
So the y intercept is 5 (not 4)
since m = -1/4 and b = 5 we go from
y = mx+b
to
y = (-1/4)x+5
So the final answer is y = (-1/4)x+5 which can be written as [tex]y = -\frac{1}{4}x+5[/tex]
As a check, we can plug x = 16 into the equation to get...
y = (-1/4)*x + 5
y = (-1/4)*16 + 5
y = -4 + 5
y = 1
so that confirms we have the right answer.
