Equation of a line (Point/Slope)

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Find the equation of the line with slope $m=-\frac{3}{2}$ and passsing through the point $P\left(2,-\frac{1}{5}\right).$

**Answer**

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 $m=-\frac{3}{2}$, $x_0=2$ and $y_0=-\frac{1}{5}$

Substituting these values in the equation, we get

$ y-(-\frac{1}{5})=-\frac{3}{2}(x-(2))$

or, $ y+\frac{1}{5}=-\frac{3}{2}(x-2)$

or, $y+\frac{1}{5}=-\frac{3}{2}x+3$

or, $y=-\frac{3}{2}x+\frac{14}{5}$