Eliminate the Parameter and Write the Corresponding Rectangular Equation Whose $\begin{array} { l } x = | t - 1 | \\y = t + 5\end{array}$

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. $\begin{array} { l } x = | t - 1 | \\y = t + 5\end{array}$

A) $x = | y - 1 | \text { OR } y = x + 1 , x \geq 0 \text { and } y = - x + 6 , x \geq 0$
B) $x = | y - 6 | \text { OR } y = x + 6 , x \geq 0 \text { and } y = - x + 6 , x \geq 0$
C) $x = | y + 6 | \text { OR } y = x + 6 , x \geq 0 \text { and } y = x + 6 , x \geq 0$
D) $x = | y - 5 | \text { OR } y = x + 5 , x \geq 0 \text { and } y = - x + 6 , x \geq 0$
E) $x = | y + 5 | \text { OR } y = x - 1 , x \geq 0 \text { and } y = - x + 5 , x \geq 0$