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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 $A + B+ C$.

 Jul 15, 2022
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The slope of line l_1 is (-5 - 3)/(2 - (-3)) = -8/5.  Then by point-slope form, the equation is

y + 3 = -8/5 (x + 3)

Multiply by 5:

5y + 15 = -8(x + 3)

Expand:

5y + 15 = -8x - 24

Simplify:

8x + 5y = -39

 

Then A + B + C = 8 + 5 + (-39) = -26.

 Jul 15, 2022

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