Write the equation of a line that is perpendicular to the given line and that passes through the given point. 2x + 4y = –6; (2, 5)

You can remove a factor of 2 from the equation of the given line so it is
  x +2y = -3

You can swap the x and y coordinates, negating the new coordinate for y. Now the equation is for a perpendicular line through (0, 0).
  2x -y = 0
Translate the line to the point (2, 5) and the equation looks ike this.
  2(x-2) -(y-5) = 0
Eliminating parentheses and adding -1 gives
  2x -y = -1

The standard form equation of the line perpendicular to the given line and passing through the point (2, 5) is
  2x - y = -1