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A line passes through the points (-3,-5) and (6,1). 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  and  is positive. Find A+B+C.

 Jun 19, 2020
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First write the equation in slope-intercept form. y=mx+b, m = slope, b = y-intercept

The slope of two points \((x_{1}, y_{1}) (x_{2}, y_{2})\) is \(\frac {y_{2} - y_{1}}{x_{2}-x_{1}}\). So based on our two points (-3, -5) and (6, 1), we get that our slope equals \(\frac{2}{3}\). Plug this into m and our equation looks like this: y=\(\frac{2}{3}\)x+b.

Now to find b, plug in one of the given points into x and y. I chose to plug in (6,1).

1=\(\frac{2}{3}\)*6+b. We find that b = -3.

This is our equation now: y = \(\frac{2}{3}\)x-3. Since the question is asking for the form Ax+By=C, we multiply by 3 to get rid of the fraction: 3y=2x-9.

Rearrange to get 2x-3y=9, where A=2, B=-3, and C=9. 

Add these numbers up to get A+B+C :)

 

EDIT: I messed up on some basic arithmetic. I fixed my answer now. 

 Jun 19, 2020
edited by thelizzybeth  Jun 19, 2020

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