I need help to find the correct answer. Can you help me with these. I would appreciate that very much

Given
Line is perpendicular to line
[tex]y=\frac{1}{4}x-1[/tex]and passes through point (4 , 1)
Find
Equation of line in slope intercept form
Explanation
Slope of given line is 1/4
let slope of perpendicular line be m
then
[tex]\begin{gathered} m\times(\frac{1}{4})=-1 \\ m=-4 \end{gathered}[/tex]then equation of line with slope will be
[tex]y=-4x+b[/tex]the above line is passing through (4 , 1)
so ,
[tex]\begin{gathered} 1=-4(4)+b \\ 1=-16+b \\ b=17 \end{gathered}[/tex]so , the required equation of line is
[tex]y=-4x+17[/tex]Final Answer
Therefore , the required equation of line is y = -4x + 17