Question

if the tangent line to y= f(x) at (4, -5) passes through the point (1,1), find f(4) and the equation of the tangent line at 4

Answer 1

to define any line you need two points. In your problem you got that: 1 point is the point of tngency (4,-5), the other is (1,1).
So your line is: (y,x)=(1,1)+c(4-1,-5-1)

Answer 2

how did u arrive at that please? i wanna know it

Answer 3

the equation of the line I wrote you is in solcolled point vector form, where point is (1,1) and direction vector is (4-1,-5-1), and c is arbitrary real constant