The equation is given as
[tex]y=\frac{1}{2}x+4[/tex]For finding the perpendicular line,
The product of slope is -1.
For the given equation , the slope is 1/2.
Now find the slope of perpendicular line.
[tex]\frac{1}{2}\times m=-1[/tex][tex]m=-2[/tex]Hence the slope of perpendicular line is -2.
Now the perpendicular equation to the given line can be
y=-2x+b.
Where assume b=1.
Then the equation perpendicular to the given line is
[tex]y=-2x+1[/tex]