Chapter 1.1, Problem 78E

a.

To determine

To find: the equation of parallel line.

Explanation of Solution

Given:

The equation is $x+5=0.....(1)$

Point is given as $(-2,4)$ .

Approach:

1. Compare with slope − intercept form of equation $y=mx+c.....(2)$
2. Find the value of slope and y-intercept.

Calculation:

Consider, $x+5=0$

  $\text{m=1}\text{and}\text{point}\text{(-2,4)}$

The slopes of parallel lines are equal. But in this equation the value of y=0 .

Putting the value $m=1,y=0\text{and}x=-2$

  $\begin{array}{l}0=mx+c\\ 0=1(-2)+c\\ c=2\end{array}$

Putting the value of c and $y=0$ in equation (2) ,

  $x+2=0$

Therefore, the equation of parallel line is $x+2=0$

b.

To determine

Write the equation of the perpendicular line.

Explanation of Solution

Given:

The equation is given as $x+5=0$

Point is given as $(-2,4)$ .

Approach:

1. Compare with slope − intercept form of equation $y=mx+c.....(2)$
2. Find the value of slope and y-intercept

Calculation:

Consider, $x+5=0$

The perpendicular slope will be the opposite reciprocal of the original slope. In the given equation the value of y=0 . So we are using x=0 for the perpendicular equation.

  $\text{m=-1}\text{and}\text{point}\text{(-2,4)}$

Putting the value of slope and $x=-2,\text{and}y=0$

  $\begin{array}{l}y=mx+c\\ 4=-1(0)+c\\ c=4\end{array}$

The above equations are shown in the graph below,

  

Therefore, the perpendicular equation of line is $y-4=0$ .