Equation of a line (Point/Slope)

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Find the equation of the line with slope $m=-\frac{1}{9}$ and passsing through the point $P\left(-\frac{7}{10},-\frac{1}{3}\right).$

**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 $m=-\frac{1}{9}$, $x_0=-\frac{7}{10}$ and $y_0=-\frac{1}{3}$

Substituting these values in the equation, we get

$ y-(-\frac{1}{3})=-\frac{1}{9}(x-(-\frac{7}{10}))$

or, $ y+\frac{1}{3}=-\frac{1}{9}(x+\frac{7}{10})$

or, $y+\frac{1}{3}=-\frac{1}{9}x-\frac{7}{90}$

or, $y=-\frac{1}{9}x-\frac{37}{90}$