Question

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

Short answer

The parametric equation is$x=t+2,y=t,0\le t\le 5$

Step-by-step solution

Step 1. Given Information

We are given a curve

Step 2. Finding Slope

The coordinates of the graph are $\left(x_1,y_1\right)=\left(2,0\right)$and $\left(x_2,y_2\right)=\left(7,5\right)$

Then, slope is$m=\frac{5-0}{7-2}=1$

Step 3. Finding linear equation

By using

$$\begin{gathered} y=mx+b \\ y=1x+\left(-2\right) \\ y=x-2 \end{gathered}$$

This is the rectangular equation that represents the given graph.

Step 4. Finding Parametric Equations

Let us consider $y=t$,$0\le t\le 5$

From $y=x-2$we get $t=x-2$

or$x=t+2$