Chapter 8.6, Problem 2CFU

To determine

To describe: the method to find parametric equations for a line passing through a given point and parallel to a given vector.

Answer to Problem 2CFU

  $\begin{array}{c}x=3+t\\ y=6+2t\end{array}$

Explanation of Solution

Given information:

  $\begin{array}{l}\left(3,6\right)\\ \overrightarrow{v}=\overrightarrow{i}+2\overrightarrow{j}\end{array}$

Calculation:

The coefficient $\overrightarrow{i}$ tells the rate at which $x$ changes over time $t$ . So, the $x$ coordinate of the given point can be used to find horizontal component of the vector as follows:

  $\begin{array}{c}x=x_1+t{a}_1\\ =3+t\left(1\right)\\ =3+t\end{array}$

The coefficient $\overrightarrow{j}$ tells the rate at which $y$ changes over time $t$ . So, the $y$ coordinate of the given point can be used to find vertical component of the vector as follows:

  $\begin{array}{c}y=y_1+t{a}_2\\ =6+t\left(2\right)\\ =6+2t\end{array}$

Thus the parametric equations for a line parallel to the given line and passing through the given point are $x=3+t$ and $y=6+2t$ .