Chapter 8.6, Problem 20E

To determine

To find: parametric equation of a line with the given equation.

Answer to Problem 20E

  $\begin{array}{c}x=t\\ y=2t-3\end{array}$

Explanation of Solution

Given information:

  $2x-y=3$

Calculation:

In a parametric equation $t$ is an independent variable whereas $x\text{ and }y$ are dependent variables.

So put $x=t$ in the given equation and solve $y$ as shown below.

  $\begin{array}{c}2x-y=3\\ 2\left(t\right)-y=3\left[\text{Add }\left(y-3\right)\text{ on each side}\right]\\ 2t-3=y\\ or\\ y=2t-3\end{array}$

Thus the parametric equations are as follows:

  $\begin{array}{c}x=t\\ y=2t-3\end{array}$