Equation of a line (Point/Slope)
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Question

Find the equation of the line with slope $m=-\frac{8}{3}$ and passsing through the point $P\left(-\frac{8}{9},-\frac{1}{2}\right).$

The equation of the line with slope $m$ and passing through the point $(x_0,y_0)$ is given by $$y-y_0=m(x-x_0)$$

Here $m=-\frac{8}{3}$, $x_0=-\frac{8}{9}$ and $y_0=-\frac{1}{2}$

Substituting these values in the equation, we get

$y-(-\frac{1}{2})=-\frac{8}{3}(x-(-\frac{8}{9}))$

or, $y+\frac{1}{2}=-\frac{8}{3}(x+\frac{8}{9})$

or, $y+\frac{1}{2}=-\frac{8}{3}x-\frac{64}{27}$

or, $y=-\frac{8}{3}x-\frac{155}{54}$