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. 


Here is what I have got so far: In the problem it says that  is parallel to our graph, Ax+By=3. Obviously, graphs that are parallel must have the same slope. Now, we should turn  into slope form. Divide everything by 3. Y=-x/3-5/3. Therefore, we have a slope of -1/3. So now we have -1/3x+By=3. Now we have got a as -1/3. Now we have to find B. We can substitute the point -7,2 into the equation. This will get us 7/3+2B=3. This will get B as 1/3. Now we need to do B-A 1/3-(-1/3). This will get us 2/3 and that is marked as wrong.

 Jun 2, 2022

The error in your work is that you substitute \(-{1 \over 3}\) for \(A\).


To avoid this error, you should first solve for the line of the equation in slope-intercept form, then convert it into standard form. 


Let the line of the equation be \(y = mx + b\). We already know that the slope is \(-{1 \over 3}\), so we can substitute that in for m. 


This gives us: \(y = -{1 \over 3}x + b\). Now, plug in the point \((-7,2)\). This gives us: \(2 = -{1 \over 3} \times 7 + b\), and we can solve for b, giving us \(b = - {1 \over3}\).


Now we have the equation: \(y = -{1 \over 3} x - {1 \over 3}\)


Can you take it from here?

 Jun 2, 2022

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