Answer:
3x -2y = -1
Explanation:
It is often convenient to start with point-slope form when you are given a point and slope. That form can be written ...
... y = m(x -h) +k . . . . . . . for slope m and point (h, k)
Given your values, this is ...
... y = (3/2)(x +3) -4
Multiplying by 2 gives ...
... 2y = 3(x +3) -8
... 0 = 3x -2y +1 . . . . eliminate parenthses, subtract 2y
... 3x -2y = -1 . . . . . . . subtract the constant to put into standard form
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Comment on standard form
Standard form requires the leading coefficient be positive and the coefficients be relatively prime. The variable terms are on one side of the equal sign, and the constant term is on the other side.
Since we wanted to write this with the variables in alphabetical order, we left the positive x term on the right side of the equation and subtracted the y term. The equation could also be written in standard form as ...
... 2y - 3x = 1
This latter form satisfies the problem requirements and would have required less manipulation, but is less pleasing, IMO.