How do i write this equation in standard form (3,-9) and parallel to 2x+3y=-12?

2 Answers

Atul Chhotray Profile
Atul Chhotray answered
The general equation of a straight line is ax+by+c = 0 where the slope of the line is -a/b.

The line in question is parallel to the line 2x + 3y - 12 = 0. The slope of this line is -2/3. As the lines are parallel so they have the same slopes.

Therefore the line we are looking for is the form of 2x + 3y + c = 0. As this line passes through the point (3,-9), putting these coordinates in the equation of the line will satisfy it.
So we have 2(3) + 3 (-9) + c =0 => 6-27+c=0 => c = 21
So the equation of the line is

2x + 3y + 21 = 0.
thanked the writer.
Oddman commented
You have identified a "general equation", but it is not "standard form." For standard form, the constant must be on the other side of the equal sign.
Oddman Profile
Oddman answered
For a parallel line in standard form, leave the x and y coefficients alone, and determine the constant required to have the equation satisfied at your point.
  2x + 3y = ?
  2(3) + 3(-9) = 6 - 27 = -21

Your equation is
  2x + 3y = -21

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