Question

Consider the line 9x-6y=-5. Find the equation of the line that is perpendicular to this line and passes through the point (-8,-2) . Find the equation of the line that is parallel to this line and passes through the point (-8,-2) .

Answer 1

• perpendicular: 2x+3y = -22
• parallel: 3x-2y = -20

Explanation:

When you have an equation of the form ...

ax -by = c

The perpendicular line will have the form ...

bx +ay = c . . . . . where the value of c makes the equation true at the given point.

The same is true for a parallel line. It will have the original coefficients, but a new value of c that makes the equation true at the desired point.

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Perpendicular:

6x +9y = 6(-8) +9(-2) = -48 -18

6x +9y = -66

2x +3y = -22 . . . . . divide by 3 to get standard form

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Parallel:

9x -6y = 9(-8) -6(-2) = -72 +12

9x -6y = -60

3x -2y = -20 . . . . in standard form

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Additional comment

The equation is in standard form when the coefficients are mutually prime. Here, that means we need to remove a factor of 3 from the coefficients we used from the original equation.