Find a rectangular equation for the plane curve defined by the parametric equations.
-$$x = t ^ { 3 } + 1 , y = t ^ { 3 } - 10 ; - 2 \leq t \leq 2$$
A) $y = x - 11$; for $x$ in $- 7 \leq x \leq 9$
B) $y = - x - 11$; for $x$ in $- 7 \leq x \leq 9$
C) $y = x ^ { 3 }$; for $x$ in $- 3 \leq x \leq 1$
D) $y = - x ^ { 2 }$; for $x$ in $- 4 \leq x \leq 4$

Question

Quizplus · Accepted Answer

Given $x = t^3 + 1$ and $y = t^3 - 10$, we can eliminate the parameter $t$ by observing that both $x$ and $y$ are defined in terms of $t^3$. Subtracting the equation for $y$ from the equation for $x$ gives $x - y = 11$, or equivalently, $y = x - 11$. The range for $x$ is determined by substituting the bounds of $t$ into the equation for $x$, yielding $x$ values from $-7$ to $9$.

Find a Rectangular Equation for the Plane Curve Defined by the Parametric