Find B-A if the graph of Ax+By=3 passes through (-7,2) and is parallel to the graph of X+3y=-5
Ax + By = 3
The slope of this line = -A/B
And
Since this line passes through (-7, 2) it must be that
A(-7) + B(2) = 3
-7A + 2B = 3
2B = 3 + 7A
B = [ 3 + 7A ] / 2
And
x + 3y = - 5
3y = -x - 5 divide both sides by 3
y = (-1/3) - 5/3
The slope of this line = (-1/3) and since this line is parallel to the first line we have that
-A/ B = -1/3
A / B = 1 / 3
A / [ (3 + 7A)/ 2 ] = 1 / 3
2A / ( 3 + 7A ) = 1/3 cross-multiply
3 * 2A = 1 ( 3 + 7A)
6A = 3 + 7A
-A = 3
A = -3
B = (3 + 7A) / 2 = ( 3 + 7(-3)) / 2 = -18/2 = -9
So
A = -3
B = -9
B - A = -9 - (-3) = -6