Equation of a line (Point/Point)
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Question

Find the equation of the line passsing through the Points $P\left(-14,-17\right)$ and $Q\left(-11,0\right)$.

Answer

The slope of the line joining the points $P\left(-14,-17\right)$ and $Q\left(-11,0\right)$ is given by $m=\frac{0+17}{-11+14}=\frac{17}{3}$

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

$y =\frac{17}{3}x-17-\left(\frac{17}{3}\right)\left(-14\right)$

or, $y =\frac{17}{3}x-17+\frac{238}{3}$

or, $y=\frac{17}{3}x+\frac{187}{3}$