A line passes through the points (-3,-5) and (8,7). The equation of this line can be expressed in the form Ax + By = C, where A, B, and C are integers with greatest common divisor 1 and A is positive. Find A + B + C.
+781 We use the given points to write an equation in slope intercept form. Using the slope formula, the slope of this line is 2/11. We currently have the equation y=2/11x+b. We plug in one of the points into the equation to find b. Using (8, 7) will be easier.
y=2/11x+b
7=2/11(8)+b
7=16/11+b
b=61/11
So the slope intercept equation we have is y=2/11x+61/11. We then convert it into standard form.
y=2/11x+61/11
-2/11x+y=61/11
2x-11y= -61
A+B+C=2+(-11)+(-61)=2-11-61= -70.
