Equation of a line (Point/Point)

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Find the equation of the line passsing through the Points $P\left(-8,-5\right)$ and $Q\left(-9,-2\right)$.

**Answer**

The slope of the line joining the points $P\left(-8,-5\right)$ and $Q\left(-9,-2\right)$ is given by $m=\frac{-2+5}{-9+8}=-3$

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

$y =-3x-5-\left(-3\right)\left(-8\right)$

or, $y =-3x-5-24$

or, $y=-3x-29$