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
From x + 3y = -5, y = -x/3 - 5, so the slope of the line is -1/3. The slope of the new line is also -1/3, so y = -x/3 + B. Pugging in x = 2 and y = -7, we get -7 = -2/3 + B, so B = -19/3.
Then the line is y = -x/3 - 19/3. Then 3y = -x - 19, so 3y + x = -19. We want the right-hand side to be 3, so we mutiply both sides by -3/19: -9/19*y - 3/19*x = 3. Therefore, B - A = -19/3 - 3 = -28/3.
Rewrite the equations as:
y = -(A/B)x + 3/B and y = -(1/3)x - 5/3
The values multiplying the x term constitute the slope.
Parallel lines have the same slope, so A/B = 1/3 or B = 3A
Since the first line passes through (-7, 2) we must have 2 = -(A/B)*(-7) + 3/B or 2 = -(A/3A)*(-7) + 3/(3A) or 2 = 7/3 + 1/A
Rearrange this last equation to find A, then find B (from B = 3A), then you can find B-A.