Chapter 8.6, Problem 1CFU

To determine

To Find: The description for the graph of the parametric equation.

Answer to Problem 1CFU

Theconsidered parametric equations describe the line passes through $P\left(x_1,y_1\right)$ is equal $\left(3,-1\right)$ and parallel to the vector $\overline{a}=\langle a_1,a_2\rangle$ that is $\langle 4,2\rangle$ .

Explanation of Solution

Given:

The given equations is,

  $\begin{array}{l}x=3+4t\\ y=-1+2t\end{array}$

Calculation:

Consider the given equation is,

  $\begin{array}{l}x=3+4t\\ y=-1+2t\end{array}$

Compare the equations with the standard equations $x_i+t_{a_1}$ and $y_1+t{a}_2$ then,

  $x_1=3$ , $y_1=-1$ , $a_1=4$ , and $a_2=2$

Therefore, the considered parametric equations describe the line passes through $P\left(x_1,y_1\right)$ is equal $\left(3,-1\right)$ and parallel to the vector $\overline{a}=\langle a_1,a_2\rangle$ that is $\langle 4,2\rangle$ .