Question

graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of curve. Verify your graph using a graphing utility.
$x=3t+2,y=t+1;0\le t\le 4$

Short answer

The Rectangular form of the given curve is $x-3y+1=0$

Orientation is Left to Right

Step-by-step solution

Step. 1 Description

Given

The parametric equation curve

$x=3t+2,y=t+1;0\le t\le 4$

To Find

a. The Rectangular equation of the given curve

b. Plot the graph of the curve and Varify it using graphing utility

Step. 2 Simplification

a. $$\begin{gathered} x=3t+2;0\le t\le 4 \\ t=\frac{x-2}{3}eqn1 \\ y=t+1;0\le t\le 4 \\ putthevalueoftfromeqn1 \\ y=\frac{x-2}{3}+1 \\ y=\frac{x+1}{3} \\ x-3y+1=0 \\ thisistherec\tan gularformofthegivenequation \end{gathered}$$

Step. 3 Simplification

The graph of given parametric equation is plotted as

Step. 3 Simplification

Hence the graph of rectangular equation of the given curve is plotted as