Answer: 3x + 2y = -22
Solving that for y leads to y = (-3/2)x - 11
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Step-by-step explanation
Anything parallel to Ax+By = C is of the form Ax+By = D where C ≠ D.
If C = D, then the two lines would be identical, so that's why we need C and D to be different values.
So anything parallel to 3x+2y = 5 is of the form 3x+2y = D, where D ≠ 5.
To find the value of D, plug in the coordinates of the given point.
3x+2y = D
D = 3x+2y
D = 3*(-2)+2*(-8)
D = -6 - 16
D = -22
Therefore, 3x+2y = -22 is parallel to 3x+2y = 5, and this parallel line goes through (-2,-8)
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Optionally we could solve for y as shown here.
3x + 2y = -22
2y = -3x - 22
y = (-3x - 22)/2
y = (-3x)/2 - 22/2
y = (-3/2)x - 11
This equation has slope -3/2 and y intercept -11.
I used GeoGebra to confirm the answer is correct.