What does the equation $\;$ $4x - 7y + 11 = 0$ $\;$ become when the origin is shifted to $\left(-3, -4\right)$.
Given equation of line: $\;$ $4x - 7y + 11 = 0$ $\;\;\; \cdots \; (1)$
The required equation is obtained by replacing $x$ by $\left(x - 3\right)$ and $y$ by $\left(y - 4\right)$ in equation $(1)$.
$\therefore \;$ The required equation is
$4 \left(x - 3\right) - 7 \left(y - 4\right) + 11 = 0$
i.e. $\;$ $4x - 12 - 7y + 28 + 11 = 0$
i.e. $\;$ $4x - 7y + 27 = 0$