Hi, i have a Problem finding a nice solution with mathematica. The Problem: I want to find all coordinates where a linear equation matches a polynom. I tried it with findroot, but that didnt bring the result i need. My Solution so far is shown below. The problem with findroot is that i have to give a starting point and that i only get one point close to the starting point. Maybe somebody can give me a hint what to do. Thank You!           Remove["Global`*"]
Points = {{0,
    0}, {1, -1}, {2, -2}, {3, -4}, {4, -3}, {5, -4}, {6, -1}, {7, \
-4}, {8, 2}, {9, 3}, {10, -1}, {11, -4}};
f = Interpolation[Points,
   InterpolationOrder -> 1](*Polynom from Points*);

\ = 45 °; (*Angle of Linear*)
fg[x_, Pos_] := -x*Tan[\] + Points[][[2]] +
  Points[][[1]]*
   Tan[\] (*Linear equation throug point (Points), gradient \
from \  *)
Plot[{fg[x, 9], f}, {x, 0, 11}, Epilog -> Map[Point, Points],
ImageSize -> Large, AspectRatio -> 1] (*Plot*)

sol = FindRoot[fg[x, 9] == f, {x, 8}, AccuracyGoal -> 8,
   PrecisionGoal -> 8];
solution = x /. sol
(*Check*)
f == fg[solution, 9]
f