Equation of a line (Point/Point)

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Find the equation of the line passsing through the Points $P\left(7,5\right)$ and $Q\left(12,-17\right)$.

**Answer**

The slope of the line joining the points $P\left(7,5\right)$ and $Q\left(12,-17\right)$ is given by $m=\frac{-17-5}{12-7}=\frac{-22}{5}$

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

$y =-\frac{22}{5}x+5-\left(-\frac{22}{5}\right)\left(7\right)$

or, $y =-\frac{22}{5}x+5+\frac{154}{5}$

or, $y=-\frac{22}{5}x+\frac{179}{5}$