Equation of a line (point/perpendicular line)
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Question

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

The slope of the line $2x-2y-9= 0$ is given by $m = 1$

The second line is parallel to this line. So, they have the same slopes $m=1$

The second line passes through the point $\left(0,0\right)$ and has slope $m=1$

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 $m=1$, $x_0=0$ and $y_0=0$

Substituting these values in the equation, we get

$y-\left(0\right)=\left(x-\left(0\right)\right)$

or, $y=\left(x\right)$

or, $y=x$