+144 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 \(A + B + C\).
+9466 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
