Circles1 with maximum and minimum values

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I have a question regarding the maximum and minimum values of $y-3x+4$ for which point $(x,y)$ moves along circle $(x-2)^2+y^2=1$. I can calculate the question but I do not know where to locate the maximum and minimum values on the graph.

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Approach the problem geometrically:

  1. Find the intersections point(s) between line and circle (solve system of equations).
  2. If there are two points, the max will occur at the right point (bc line has positive slope).
  3. If there is only one intersection, the single intersection point will be the maximum (tangent to circle).

Also, the max value is not $-2+\sqrt{10}$ as you can see in picture.

enter image description here