Question

Eliminate the parameter t. Find a rectangular equation for the pane curve defined by parametric equations (check image)

Answer 1

Given

`\begin{gathered} x=3t...Equation\text{ i} \\ y=t+3...\text{ Equation ii} \\ \\ -2\leq t\leq3 \end{gathered}`

Make t the subject

`\begin{gathered} x=3t \\ t=(x)/(3) \end{gathered}`

Substitute for t in equation ii

`y=(x)/(3)+3`

Substitute for t in the given range

`\begin{gathered} -2\leq t\leq3 \\ -2\leq(x)/(3)\leq3 \\ \\ clear\text{ the fraction by multiply all through by 3} \\ -6\leq x\leq9 \end{gathered}`

The final answer

Option C