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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.

 Jun 27, 2021
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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

 Jun 27, 2021

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