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The line \( l_1\) passes through the points \((3,-3) \)  and \((-5,2)\) . The line is the graph of the equation \(Ax + By = C\), where \(A\), \(B\) , and \(C\)  are integers with greatest common divisor 1, and A is positive. Find \(A + B + C\).

HelpPLZ  Sep 28, 2018
 #1
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slope of the line that passes through  (3, -3)  and  (-5, 2)   =   \(\frac{y_2-y_1}{x_2-x_1}\,=\,\frac{2--3}{-5-3}\,=\,-\frac{5}{8}\)

 

The line  l1  passes through the point  (3, -3)  and has a slope of  \(-\frac58\)   .

So the equation of  l1 in point-slope form is...

 

y - -3  =  \(-\frac58\)(x - 3)       Now we just have to get this equation in the form Ax + By  =  C

 

y + 3  =  \(-\frac58\)(x - 3)

                                     Multiply both sides of the equation through by  8 .

8y + 24  =  -5(x - 3)

                                     Distribute the  -5  to the terms in parenthesees.

8y + 24  =  -5x + 15

                                     Subtract  24  from both sides of the equation.

8y  =  -5x + 15 - 24

 

8y  =  -5x - 9

                                     Add  5x  to both sides of the equation.

5x + 8y  =  -9

 

5 ,  8 , and  -9  are integers with the greatest common divisor  1 , and  5  is positive.

 

5 + 8 + -9   =   4

hectictar  Sep 29, 2018

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