Chapter SH, Problem 4.4.3EP

To determine

Equation for the line parallel to the given line and line perpendicular to the given line.

Answer to Problem 4.4.3EP

The equation of parallel line will be:

  $y=\frac{2}{3}x+2$

The equation of perpendicular line will be:

  $y=-\frac{3}{2}x-\frac{9}{2}$

Explanation of Solution

Given:

The given data is:

  $\left(-3,0\right),y=\frac{2}{3}x+1$

Calculation:

The point slope form is $y-y_1=m\left(x-x_1\right)$

Parallel lines have same slope and the perpendicular lines have slope of negative reciprocal to each other.

The equation of parallel line will be:

  $\begin{array}{l}y-0=\frac{2}{3}\left(x-\left(-3\right)\right)\\ y=\frac{2}{3}x+2\end{array}$

The equation of perpendicular line will be:

  $\begin{array}{l}y-0=-\frac{3}{2}\left(x-\left(-3\right)\right)\\ y=-\frac{3}{2}x-\frac{9}{2}\end{array}$