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# Stuck on problem :(

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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.

Aug 15, 2020

#1
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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.

Aug 15, 2020
#2
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that's not right, but thank you anyways!!!

Aug 16, 2020
#3
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Let's see who I agree with.

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.

parallel to the graph of x + 3y = -5.

$$3y=-x-5\\ y=-\frac{1}{3}x-\frac{5}{3}\\ \text{So the gradient of the line = } -\frac{1}{3}$$

The line will be

$$y=\frac{-1x}{3}+b\\ Sub\;\;in\;\;(-7,2)\\ 2=\frac{--7}{3}+b\\ 2-\frac{7}{3}=b\\ b=\frac{-1}{3}\\ y=\frac{-1x}{3}+\frac{-1}{3}\\ 3y=-x-1\\ 3y+x=-1\\ -9y-3x=+3\\ A=-9,\quad B=-3\\ B-A=-3--9=6$$

Aug 21, 2020