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.
+240 Putting the equations into slope-intercept form,
\(y = -\frac{Ax}{B} + \frac{3}{B}\)
\(y = -\frac{x}{3} - \frac{5}{3}\)
Both lines are parallel, so \(-\frac{x}{3} = -\frac{Ax}{B}\). Simplify to find that \(\frac{A}{B} = \frac{1}{3}\), meaning that the slope is \(-\frac{1}{3}\).
\(y = -\frac{x}{3} + \frac{3}{B}\)
Plug in (-7, 2).
\(2 = -\frac{-7}{3} + \frac{3}{B}\)
\(6B = 7B + 9\)
\(B = -9\)
Because A and B are in ratio \(\frac{A}{B} = \frac{1}{3}\), B = -9 and A = -3. So B - A = -9 - (-3) = -6
+37159 x + 3y = -5 re arrange to y = mx+b from:
y = -1/3 x - 5/3 slope = -1/3 ( parallel slope is the same)
y = -1/3 x - b sub in the given point to calculate 'b'
2 = -1/3 (-7) + b shows b = - 1/3
y = -1/3 x - 1/3 multiply by 3 to get rid of fraction
3y = 3x - 3
3x -3y = 3 then B - A = -3 - 3 = - 6
