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 A line passes through the points $P$ and $Q.$  If $P = (-8,2)$ and $Q = (1,7),$ 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.

 Oct 5, 2023
 #1
avatar+14944 
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Write the equation in the form $Ax + By = C.

 

Hello tomtom!

 

P(-8,2)

Q(1,7)

\(m=\frac{y_P-x_P}{y_Q-x_Q}=\frac{2-(-8)}{7-1}=\frac{5}{3}\\ y=m(x-x_Q)+y_Q\\ y=\frac{5}{3}(x-1)+7\\ y=\frac{5}{3}x-\frac{5}{3}+7\\ -\frac{5}{3}x+y=\frac{16}{3}\ |\ \cdot (-3)\\ \color{blue}5x-3y=-16\)

laugh  !

 Oct 5, 2023

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