Write an equation perpendicular to the line y=1/4x -9 and passes through (1,1)can someone me with this (explain it)

Whenever we have a perpendicular line, the new slope is always going to be the opposite of the reciprocal of the old slope. Therefore, this new slope will be -4. The way to check is to multiply them together, and if you get -1, then you are correct. Now, we will use our points to find b, or the y-intercept. We can do 1 = -4(1) + b. What I did here was plugged in the values from the points you have provided. Now, I have 1 = -4 + b. I add 4 to both sides, and I know b = 5. Therefore, my new equation is y = -4x +5. Hope this helps!