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) $x = | y + 5 | \text { OR } y = x - 1 , x \geq 0 \text { and } y = - x + 5 , x \geq 0$

Question

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) $x = | y + 5 | \text { OR } y = x - 1 , x \geq 0 \text { and } y = - x + 5 , x \geq 0$

Quizplus · Accepted Answer

To eliminate the parameter, solve for $t$ in terms of $y$: $t = y - 5$. Substitute into $x = |t - 1|$: $x = |y - 6|$. The graph is a V-shape with vertex at $y = 6$, so $y = x + 6$ for $x \geq 0$ and $y = -x + 6$ for $x \geq 0$.

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

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