Q.Find the equation of the line passing through $(4, 5)$ and parallel to the line $2x - y + 3 = 0$.

A parallel line keeps the same $x,y$ coefficients: $2x - y + k = 0$; find $k$ from the given point.

A line parallel to $2x - y + 3 = 0$ has the same coefficients of $x$ and $y$, so write it as

Since it passes through $(4, 5)$:

Hence the line is $2x - y - 3 = 0$. …

Reusing the original constant $3$ instead of solving for $k$ (here $k$ happens to also be $3$, but only because of the specific point — it must alw …