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Find B - A if the graph of Ax + By = 3 passes through (-7,2) and is parallel to the graph of x + 3y = -5.

 Mar 1, 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.

 Mar 1, 2020
 #2
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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.

 Mar 1, 2020

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