Equation of a line (point/point of intersection)

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Find the equation of the line passsing through the point P $\left(2,\frac{2}{5}\right)$ and the intersection of the lines $x+y+2= 0$ and $2x-3y-6= 0$

**Answer**

The lines $x+y+2= 0$ and $2x-3y-6= 0$ intersect at the point Q$\left(0,2\right)$

The given line passes through the point P $\left(2,\frac{2}{5}\right)$ and $\left(0,2\right)$

The slope of the line joining the points $P\left(2,\frac{2}{5}\right)$ and $Q\left(0,2\right)$ is given by $m=\frac{2-\frac{2}{5}}{0-2}=\frac{-4}{5}$

The $y-intercept = 2$.

So, the equation of the line is

$y=-\frac{4}{5}x+2$