Find B - A if the graph of Ax + By = 3 passes through (-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.
+23246 The original line has an equation of x + 3y = -5.
Therefore, all lines parallel to this line has an equation of this form: x + 3y = C.
Using the point (-7,2) ---> -7 + 3(2) = C ---> -7+ 6 = C ---> C = -1
This means that the new line has an equation of: x + 3y = -1
However, the constant must have value = 3; so, multiply each term of the equation by -3 ---> -3x - 9y = 3
In this equation: A = -3 and B = -9 ---> B - A = -9 - -3 = -9 + 3 = -6.
