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 $x + 3y = -5.$


Can you guys also show how you did it? 



 Sep 4, 2020

First we convert ax+by=3 into slope intercept form: -ax/b+3/b=y

We know that it is parralell to x+3y=-5 (-x/3-5/3=y in slope intercept form) so the slopes are the same. There for the slope is -1/3. 

Putting this into the 1st equations we get -1/3x+3/b=y and also putting in the point (-7,2) we get 7/3+3/b=2. 

From this we can solve that b=-9

Plugging everything (including b and point (-7,2)) back in the original equation ax+by=3, we get -7a-18=3 so a=-3

And thus b-a=-9-(-3)=-9+3=-6

So b-a is equal to -6 that is our answer

 Sep 4, 2020

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