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A line passes through the points $P$ and $Q.$ If $P = (-8,2)$ and $Q = (4,-7),$ then write the equation of this line in the form $Ax + By = C,$ where $A$, $B$, and $C$ are integers with greatest common divisor $1,$ and $A$ is positive.

 Apr 5, 2024

Best Answer 

 #1
avatar+14943 
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Write the equation of this line in the form Ax + By = C

 

\(m=\dfrac{y_p-y_q}{x_p-x_q}=\dfrac{2-7}{-8-4}=\dfrac{5}{12}\\ y=m(x-x_q)+y_q\\ y=\frac{5}{12}(x-4)-7\\ y=\frac{5}{12}x-\frac{5}{3}-7\\ -\frac{5}{12}x+y=-\frac{5}{3}-7\\ \dfrac{-5x+12y}{12}=\dfrac{-20-84}{12}\\ \dfrac{5x-12y}{12}=\dfrac{20+84}{12}\)

\(Ax+By=C\\ \color{blue}5x-12y=104\)

 

laugh !

 Apr 6, 2024
edited by asinus  Apr 6, 2024
 #1
avatar+14943 
+1
Best Answer

Write the equation of this line in the form Ax + By = C

 

\(m=\dfrac{y_p-y_q}{x_p-x_q}=\dfrac{2-7}{-8-4}=\dfrac{5}{12}\\ y=m(x-x_q)+y_q\\ y=\frac{5}{12}(x-4)-7\\ y=\frac{5}{12}x-\frac{5}{3}-7\\ -\frac{5}{12}x+y=-\frac{5}{3}-7\\ \dfrac{-5x+12y}{12}=\dfrac{-20-84}{12}\\ \dfrac{5x-12y}{12}=\dfrac{20+84}{12}\)

\(Ax+By=C\\ \color{blue}5x-12y=104\)

 

laugh !

asinus Apr 6, 2024
edited by asinus  Apr 6, 2024

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