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.
+238 Line 1 = \(x + 3y = -5\)
Line 2 = \(Ax + By = 3\)
Rearrange Line 1 into slope intercept form,
Line 1 = \(y = -x/3 - 5\)
Because Line 2 has the same slope,
Line 2 = \(y = -x/3 + b\)
Multiply Line 2 by 3 on both sides and convert to standard form,
Line 2 = \(3y = -x + 3b\)
Line 2 = \(x + 3y = 3b\)
Line 2 must pass through (-7, 2), so we can plug in these values,
Line 2 = \(-1 = 3b\)
\(b = -1/3\)
Line 2 = \(x + 3y = -1\)
Multiply both sides by -3,
Line 2 = \(-3x + -9y = 3\)
B - A = -9 - (-3) = -6
