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Explanation:
Anything perpendicular to Ax+By = C is of the form Bx-Ay = D
Note the swap of A and B, and how the plus sign changed to a minus sign.
In the case of -2x+3y = 9, we see that A = -2, B = 3, and C = 9.
So Bx-Ay = D updates to 3x-(-2)y = D which simplifies to 3x+2y = D
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To find the value of D, plug in the given point (x,y) = (-1,-3) and simplify
3x+2y = D
D = 3x+2y
D = 3(-1) + 2(-3) ... plug in x = -1, plug in y = -3
D = -3 - 6
D = -9
Now we can say 3x+2y = D turns into 3x+2y = -9
Therefore, the line that is perpendicular to -2x+3y = 9 and it goes through (-1,-3) is 3x+2y = -9
