Chapter 9, Problem 63RE

To determine

Find the points for the set of parametric equations and also sketch the graph for this.

Answer to Problem 63RE

The points for the parametric equations are $(-8,15),(-5,11),(-2,7),(1,3),(4,-1),(7,-5)$ .

Explanation of Solution

Given: It is given in the question that the parametric equations are $x=3t-2,y=7-4t$ .

Concept Used:

In this, use the concept of putting the different value in the above equation and get the coordinates.

Calculation:

Here, the equation are $x=3t-2,y=7-4t$ .

  $\begin{array}{l}Putx,y=-2\\ x=3(-2)-2=-6-2=-8\\ y=7-4(-2)=7+8=15\end{array}$

  $\begin{array}{l}Putx,y=-1\\ x=3(-1)-2=-3-2=-5\\ y=7-4(-1)=7+4=11\end{array}$

  $\begin{array}{l}Putx,y=0\\ x=3(0)-2=-2=-2\\ y=7-4(0)=7\end{array}$

  $\begin{array}{l}Putx,y=1\\ x=3(1)-2=3-2=1\\ y=7-4(1)=7-4=3\end{array}$

  $\begin{array}{l}Putx,y=2\\ x=3(2)-2=6-2=4\\ y=7-4(2)=7-8=-1\end{array}$

  $\begin{array}{l}Putx,y=3\\ x=3(3)-2=9-2=7\\ y=7-4(3)=7-12=-5\end{array}$

Now, the graph for the given points is given below:

  

Conclusion:

The points are $(-8,15),(-5,11),(-2,7),(1,3),(4,-1),(7,-5)$ .