Answer:
- perpendicular: 2x+3y = -22
- parallel: 3x-2y = -20
Step-by-step 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.
