Chapter 8.6, Problem 19E

To determine

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

Answer to Problem 19E

  $\begin{array}{c}x=t\\ y=\frac{3}{4}t+\frac{7}{4}\end{array}$

Explanation of Solution

Given information:

  $-3x+4y=7$

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.

  $\begin{array}{c}-3\left(t\right)+4y=7\\ 4y=3t+7\\ y=\frac{3}{4}t+\frac{7}{4}\end{array}$

Thus the parametric equations are as follows:

  $\begin{array}{c}x=t\\ y=\frac{3}{4}t+\frac{7}{4}\end{array}$