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Thanks for the help DRWLS. I tried to work is out and came up with this working out:
A(4,-2) is parallel to 2x-3y=7

y = mx + c
-3y = -2x + 7
y = 2/3x - 2 1/3

(y-y*) / (x-x*) = m
(y+2) / (x-4) = 2/3
y+2 = 2/3(x-4)
y+2 = 2/3x - 2 2/3
y = 2/3x-2 2/3 - 2
y = 2/3x-4 2/3

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