Chapter 11.1, Problem 1E

To determine

To Find:The equation relating $x$ , $y$ and sketch the parametric curves.

Answer to Problem 1E

Therequired answer is $y=2x-9$ .

Explanation of Solution

Given:

  $x=2t+3$  ........ (1)

  $y=4t-3$  ........ (2)

  $t\in \left[0,3\right]$

Calculation:

Substitute $0,3$ for $t$ in equation (1) and (2) to draw the graph

  $\begin{array}{l}x=2t+3y=4t-3\\ x=\left(3,9\right)y=\left(-3,9\right)\end{array}$

  

From equation (1)

  $\begin{array}{l}x=2t+3\\ t=\frac{x-3}{2}\end{array}$

From equation (2)

  $y=4t-3$

Substitute $\frac{x-3}{2}$ for $t$ in equation (2)

  $\begin{array}{l}y=4\frac{\left(x-3\right)}{2}-3\\ y=2x-9\end{array}$

Conclusion:

Hence, the required answer is $y=2x-9$ .