Given data:
The given equation of line is y=x/4+5.
The given y-intercept is (0,c)=(0,-3).
The standard equation of line is,
y=mx+c
Compare the given equation with the above expression.
m=1/4
The expression for the slope which is perpendicular to the given line.
[tex]\begin{gathered} m^{\prime}\times m=-1 \\ m^{\prime}(\frac{1}{4})=-1 \\ m^{\prime}=-4 \end{gathered}[/tex]
The equation of the line which is perpendicular to the given line is,
[tex]\begin{gathered} y=m^{\prime}x+c \\ =-4x-3 \end{gathered}[/tex]
Thus, the line which is perpendicular to the given line is y=-4x-3.
