Equation of a line (point/perpendicular line)

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Find the equation of the line passsing through the point P $\left(-1,2\right)$ and parallel to the line $x-9y-6= 0$

**Answer**

The slope of the line $x-9y-6= 0$ is given by $m = \frac{1}{9}$

The second line is parallel to this line. So, they have the same slopes $m=\frac{1}{9}$

The second line passes through the point $\left(-1,2\right)$ and has slope $m=\frac{1}{9}$

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

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

Substituting these values in the equation, we get

$ y-\left(2\right)=\frac{1}{9}\left(x-\left(-1\right)\right)$

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

or, $y-2=\frac{1}{9}x+\frac{1}{9}$

or, $y=\frac{1}{9}x+\frac{19}{9}$