Question

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 $x + 3y = -5.$

Answer 1

Answer:

Since B is equal to -9, then A must be equal to 3. "B - A" is equal to -12 The expression of the line is then: $-9x + 3y = 3$

Step-by-step explanation:

In order to solve this problem, lets first find the slope of the line. Since the line we want to know is parallel to "x + 3y = -5", then their slopes are the same, therefore:

$x + 3y = -5\\3y = -5 -x\\y = -\frac{x}{3} - \frac{5}{3}$

The slope of the line is the number that multiplies "x", therefore m = $-\frac{1}{3}$. Organizing the first equation to the form we need, gives us:

$Ax + By = 3\\By = 3 - Ax\\y = -\frac{A}{B}x + \frac{3}{B}$

We know that $-\frac{A}{B} = -\frac{1}{3}$ because the lines are parallel, if we apply the point given we will find the value of B and therefore the value of A.

$y = -\frac{1}{3}x + \frac{3}{B}\\2 = -\frac{1}{3}*(-7) + \frac{3}{B}\\2 = \frac{7}{3} + \frac{3}{B}\\\frac{3}{B} = 2 - \frac{7}{3}\\\frac{3}{B} = \frac{6 - 7}{3}\\\frac{3}{B} = \frac{-1}{3}\\B = -9$

$B - A = -9 -3 = -12$

Since B is equal to -9, then A must be equal to 3. "B - A" is equal to -12. The expression of the line is then: $-9x + 3y = 3$