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The line l 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.

Nov 10, 2018

#1
+5095
+1

pretty simple stuff

first find the slope of the line

\(m = \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{2-(-3)}{-5-3} = \dfrac{5}{-8}=-\dfrac 5 8\)

now use point slope form with say the first point (3,-3) to define the line

\((y-p_y) = m(x-p_x)\\ (y-(-3))=-\dfrac 5 8(x-3)\\ y+3 = -\dfrac 5 8(x-3)\\ y+3 = -\dfrac 5 8 x+\dfrac{15}{8}\\ 8y + 24 = -5x + 15\\ 5x+8y = -9\\ 5+8+(-9) = 4\)

.
Nov 10, 2018

#1
+5095
+1

pretty simple stuff

first find the slope of the line

\(m = \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{2-(-3)}{-5-3} = \dfrac{5}{-8}=-\dfrac 5 8\)

now use point slope form with say the first point (3,-3) to define the line

\((y-p_y) = m(x-p_x)\\ (y-(-3))=-\dfrac 5 8(x-3)\\ y+3 = -\dfrac 5 8(x-3)\\ y+3 = -\dfrac 5 8 x+\dfrac{15}{8}\\ 8y + 24 = -5x + 15\\ 5x+8y = -9\\ 5+8+(-9) = 4\)

Rom Nov 10, 2018