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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.

 Jul 4, 2020
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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.

 Jul 4, 2020
edited by gwenspooner85  Jul 4, 2020

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