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HELP ASAP

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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