Equation of a line (Point/Point)

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Find the equation of the line passsing through the Points $P\left(8,-7\right)$ and $Q\left(4,10\right)$.

**Answer**

The slope of the line joining the points $P\left(8,-7\right)$ and $Q\left(4,10\right)$ is given by $m=\frac{10+7}{4-8}=\frac{-17}{4}$

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

$y =-\frac{17}{4}x-7-\left(-\frac{17}{4}\right)\left(8\right)$

or, $y =-\frac{17}{4}x-7+34$

or, $y=-\frac{17}{4}x+27$