Chapter 8.6, Problem 35E

a.

To determine

To find: the part of the line.

Answer to Problem 35E

Right of point $\left(2,4\right)$

Explanation of Solution

Given information:

The line is obtained by assigning only negative values to $t$ .

The parametric equations of a line in a plane are as follows:

  $\begin{array}{l}x=2+3t\\ y=4+7t\end{array}$

Calculation:

Substitute $t\ge 0$ , in the parametric equations and $\left(x,y\right)$ obtained will be as follows:

  $\begin{array}{l}x\ge 2\\ y\ge 4\end{array}$

Thus, the part of line to the right of point $\left(2,4\right)$ is obtained by assigning only negative values to $t$ .

b.

To determine

To find: $t$ to give the part of line to the left of $y$ -axis.

Answer to Problem 35E

  $t<-\frac{2}{3}$

Explanation of Solution

Given information:

The parametric equations of a line in a plane are as follows:

  $\begin{array}{l}x=2+3t\\ y=4+7t\end{array}$

Calculation:

The value of $t$ to get the part of line to the left of $y$ -axis, substitute $x<0$ and evaluate $t$ as follows:

  $\begin{array}{c}2+3t<0\\ 3t<-2\\ t<-\frac{2}{3}\end{array}$

Thus, the value of $t$ to give the part of line to the left of $y$ -axis is $t<-\frac{2}{3}$ .