Question

In Problems 35–38, find parametric equations that define the curve shown.

Short answer

The parametric equation is$x=1-t,y=t,-2\le t\le 2$

Step-by-step solution

Step 1. Given Information

We are given a graph

Given the curve and its coordinates, we were asked to determine its parametric equation. To do that, we have to find equation representing the given graph to find the parametric equation.

Step 2. Finding Slope

The coordinates of the graph are $\left(x_1,y_1\right)=\left(-1,2\right)$and $\left(x_2,y_2\right)=\left(3,-2\right)$

Then, slope is$m=\frac{-2-2}{3+1}=\frac{-4}{4}=-1$

Step 3. Finding Linear Equation

By Using

$y=mx+c$

$$\begin{gathered} y=-1x+1 \\ y=-x+1 \end{gathered}$$

This is the rectangular equation.

Step 4. Finding Parametric Equation

Put $y=t,-2\le t\le 2$

From$y=-x+1$, we get$$\begin{gathered} t=-x+1 \\ x=1-t \end{gathered}$$