Equation of a line (Point/Point)
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Question

Find the equation of the line passsing through the Points $P\left(11,-6\right)$ and $Q\left(-12,13\right)$.

The slope of the line joining the points $P\left(11,-6\right)$ and $Q\left(-12,13\right)$ is given by $m=\frac{13+6}{-12-11}=\frac{-19}{23}$

The equation of the line is$$y - y_0 = m\left(x - x_0\right)$$

or, $$y= mx + y_0-mx_0$$

Substituting the values of $m$, $x_0$ and $y_0$, we get

$y =-\frac{19}{23}x-6-\left(-\frac{19}{23}\right)\left(11\right)$

or, $y =-\frac{19}{23}x-6+\frac{209}{23}$

or, $y=-\frac{19}{23}x+\frac{71}{23}$