Chapter 9, Problem 55CR

a.

To determine

To find: The values of $x\text{ and }y$ and create a table using the indicated values of $t$

Answer to Problem 55CR

The values of $x\text{ and }y$ is determines and the obtained table is

$t$	$-2$	$-1$	0	1	2
$x$	$-8$	$-5$	$-2$	1	4
$y$	15	11	7	3	$-1$

Explanation of Solution

Given information:

The values are,

  $x=3t-2,y=7-4t\text{ and }t=-2,-1,0,1\text{ and }2$

Calculation:

When $t=-2$ then the value of $x\text{ and }y$ will be,

  $\begin{array}{l}x=3t-2y=7-4t\\ x=3\left(-2\right)-2=-8\text{ and }y=7-4\left(-2\right)=15\end{array}$

When $t=-1$ then the value of $x\text{ and }y$ will be,

  $\begin{array}{l}x=3t-2y=7-4t\\ x=3\left(-1\right)-2=-5\text{ and }y=7-4\left(-1\right)=11\end{array}$

When $t=0$ then the value of $x\text{ and }y$ will be,

  $\begin{array}{l}x=3t-2y=7-4t\\ x=3\left(0\right)-2=-2\text{ and }y=7-4\left(0\right)=7\end{array}$

When $t=1$ then the value of $x\text{ and }y$ will be,

  $\begin{array}{l}x=3t-2y=7-4t\\ x=3\left(1\right)-2=1\text{ and }y=7-4\left(1\right)=3\end{array}$

When $t=2$ then the value of $x\text{ and }y$ will be,

  $\begin{array}{l}x=3t-2y=7-4t\\ x=3\left(2\right)-2=4\text{ and }y=7-4\left(2\right)=-1\end{array}$

The table for the values are

$t$	$-2$	$-1$	0	1	2
$x$	$-8$	$-5$	$-2$	1	4
$y$	15	11	7	3	$-1$

Therefore the table is obtained.

b.

To determine

To graph: The parametric equation with the use of obtained table

Explanation of Solution

Given information:

The values are,

  $x=3t-2,y=7-4t\text{ and }t=-2,-1,0,1\text{ and }2$

Graph:

  

Interpretation: The value obtained in the table is plotted and the graph is obtained.