Find a rectangular equation for the plane curve defined by the parametric equations.
-$$\mathrm { x } = 3 \mathrm { t } , \mathrm { y } = \mathrm { t } + 1 ; - 2 \leq \mathrm { t } \leq 3$$
A) $y = \frac { 1 } { 3 } x - 1$; for $x$ in $- \infty

Question

Find a rectangular equation for the plane curve defined by the parametric equations.
-$$\mathrm { x } = 3 \mathrm { t } , \mathrm { y } = \mathrm { t } + 1 ; - 2 \leq \mathrm { t } \leq 3$$
A) $y = \frac { 1 } { 3 } x - 1$; for $x$ in $- \infty < x < \infty$
B) $y = x ^ { 2 } + 1$; for $x$ in $- 2 \leq x \leq 2$
C) $y = - 3 x + 1$; for $x$ in $- \infty < x < \infty$
D) $y = \frac { 1 } { 3 } x + 1$; for $x$ in $- 6 \leq x \leq 9$

Quizplus · Accepted Answer

To find a rectangular equation, we eliminate the parameter $t$. From $x = 3t$, we get $t = \frac{x}{3}$. Substituting this into $y = t + 1$, we get $y = \frac{x}{3} + 1$, which matches option D. The domain for $x$ comes from the given range of $t$, where $x = 3t$ ranges from $-6$ to $9$ when $t$ ranges from $-2$ to $3$.

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