Find the value of $B - A$ if the graph of $Ax + By = 3$ passes through the point $(-7,2),$ and is parallel to the graph of $x + 3y = -5.$

  -6

Step-by-step explanation:

The parallel line can be written using the same x- and y-coefficients, but with a different constant:

  x +3y = constant

For the line to go through the given point, the constant must be ...

  (-7) +3(2) = constant

  -1 = constant

In order for the constant to be +3 instead of -1, the entire equation must be multiplied by -3:

  -3x -9y = 3   ⇒   A = -3, B = -9

Then the expression B-A is ...

  B -A = (-9) -(-3) = -6

The value of B - A is -6.

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