Write whether the following statements are True or False? Justify your answers.
$(i)$ The line parallel to the $y$-axis at a distance of $4$ units to the left of the $y$-axis is given by the equation $x = -4$.
$(ii)$ The graph of the equation $y = mx + c$ passes through the origin.

(A) $(i)$ True. $A$ line parallel to the $y$-axis at a distance $a$ units to the left of the $y$-axis is represented by the equation $x = -a$. Since the distance is $4$ units,the equation is $x = -4$.
$(ii)$ False. For a graph to pass through the origin $(0, 0)$,the coordinates must satisfy the equation. Substituting $x = 0$ and $y = 0$ into $y = mx + c$ gives $0 = m(0) + c$,which implies $c = 0$. Since $c$ is not necessarily $0$ for all lines of the form $y = mx + c$,the statement is false.