Equation of a line (point/perpendicular line)

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Find the equation of the line passsing through the point P $\left(\frac{10}{7},8\right)$ and parallel to the line $5x+y+2= 0$

**Answer**

The slope of the line $5x+y+2= 0$ is given by $m = -5$

The second line is parallel to this line. So, they have the same slopes $m=-5$

The second line passes through the point $\left(\frac{10}{7},8\right)$ and has slope $m=-5$

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 $m=-5$, $x_0=\frac{10}{7}$ and $y_0=8$

Substituting these values in the equation, we get

$ y-8=-5\left(x-\frac{10}{7}\right)$

or, $y-8=-5x+\frac{50}{7}$

or, $y=-5x+\frac{106}{7}$