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.

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

Short answer

Rectangular equation of the given curve is $2x-y+10=0;0\le x+3\le 2$

orientation and the graph are plotted in the solution

Step-by-step solution

Step. 1 Description

Given The parametric equation of a curve

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

To find

a. Rectangular equation of the curve

b. Graph the curve, show its orientation and varify it by graphing utility

Step. 2 Simplification

$$\begin{gathered} x=t-3 \\ t=x+3eqn1 \\ y=2t+4 \\ Putthevalueoftfromequation1 \\ y=2(x+3)+4 \\ 2x-y+10=0 \end{gathered}$$

This is the rectangular equation of the given parametric equation

Step. 3 Simplification

The graph of the parametric equation is plotted as

Step. 4 Simplification

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

Both the equations represent the same graph

Hence it is varified