Question

Write an equation that is parallel to the line 4x - y = 2 and passes through the point (-2, 3)

Answer 1

We can start from the given line's coefficients and translate the line from the origin to the given point.
  4(x -(-2)) -(y -3) = 0
  4x +8 -y +3 = 0

The equation of the desired line is ...
  4x -y = -11

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For standard form line ax+by=c, any parallel line will have only a different value of c. For c=0, the line goes through the origin (0, 0). To make it go through point (h, k) we can write it as
  a(x-h) +b(y-k) = 0
which is completely equivalent to
  ax +by = ah +bk