Chapter 10.7, Problem 8AYU

In Problems 7-26, 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.

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

To determine

To find:

a. The rectangular equation of the curve.

Answer to Problem 8AYU

$2x-y+10=0$

Explanation of Solution

Given:

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

Calculation:

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

$y=2\left(x+3\right)+4$

$y=2x+6+4$

$2x-y+10=0$

To determine

To graph:

b. $x=t-3,y=2t+4;0\le t\le 2$, verify with the graph of rectangular equation of the curve.

Answer to Problem 8AYU

Explanation of Solution

Given:

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

Graph:

The graph of $x=t-3,y=2t+4;0\le t\le 2$ is plotted.

The graph of $2x-y+10=0$; $0\le x-3\le 2$ is plotted.

Graph 1 represents the graph of $x=t-3,y=2t+4;0\le t\le 2$ plotted in parametric mode and the orientation is shown.

The rectangular equation of the curve is calculated. Graph 2 represents the curve of the rectangular equation $2x-y+10=0$.

Both the equation represents the same graph and orientation. Hence it is verified.