Question

In problem graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. Verify your graph using a graphing utility.

$x=t-3,y=2t+40\le t\le 2.$

Short answer

The answer is$y-2x-10=0.$

Step-by-step solution

Step 1. Given information.

$$\begin{gathered} x=t-3 \\ y=2t+4 \end{gathered}$$

is given.

Step 2. Calculation.

Graph the curve defined by the parametric equations -

$x=t-3y=2t+40\le t\le 2$

$t$	$x$	$y$	data-custom-editor="chemistry" $(\mathrm{x},\mathrm{y})$
$0$	$2$	1	(2,1)
1	5	2	(5,2)
2	8	3	(8,3)

We find the rectangular equation by eliminating the parameter t from the parametric equations.

$$\begin{gathered} x=t-3 \\ t=x+3 \end{gathered}$$

Put the value of t-

$$\begin{gathered} y=2t+4 \\ y=2(x+3)+4 \\ y=2x+6+4 \\ y=2x+10 \\ y-2x-10=0. \end{gathered}$$

Thus, the equation is$y-2x-10=0.$