+96 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, A + B = -9/19 - 3/19 = -12/19.
+128473 The slope of x+ 3y = -5 is -1/3
So.....the equation of a line with a slope of -1/3 and passes throiugh the point (-7,2) is
y = (-1/3)(x - - 7) + 2 simplify
y = (-1/3)x - 7/3 + 6/3
y = (-1/3)x - 1/3 multiply through by 3
3y = -x - 1 add x to both sides
x + 3y = -1
B = 3 A =1
B - A = 2
Here's a graph : https://www.desmos.com/calculator/qhp2legobe
