Question

Find the equation of the line through the points (−2,5) and (4,9).

Answer 1

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Answer:

  2x -3y = -19

Step-by-step explanation:

Taking the differences between the given points, we have ...

  (Δx, Δy) = (4, 9) -(-2, 5) = (6, 4)

The equation of the line can be written ...

  Δy·x -Δx·y = Δy·(x1) -Δx·(y1) . . . . . for point (x1, y1) on the line

  4x -6y = 4(-2) -6(5) = -38

Dividing by 2 gives the standard form equation ...

  2x -3y = -19

_____

Additional comment

The original equation 4x-6y=-38 satisfies the requirements of this problem. However, "standard form" requires the numbers in the equation be mutually prime (in addition to the problem requirements). That is, they must have no common factors. Hence, we must remove the common factor of 2 in order to have true "standard form."