Chapter 8.6, Problem 22E

To determine

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

Answer to Problem 22E

  $\begin{array}{c}x=t\\ y=-\frac{2}{3}t+\frac{11}{3}\end{array}$

Explanation of Solution

Given information:

  $2x+3y=11$

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.

  $\begin{array}{l}2x+3y=11\\ 2\left(t\right)+3y=11\\ 3y=-2t+11\left[\text{Subtract 2}t\text{ from each side}\right]\\ y=\frac{-2}{3}t+\frac{11}{3}\left[\text{Divide each side by 3}\right]\end{array}$

Thus the parametric equations are as follows:

  $\begin{array}{c}x=t\\ y=-\frac{2}{3}t+\frac{11}{3}\end{array}$