Chapter 4.3, Problem 14Q

(a)

To determine

To find: The equation for the line that passes through the given point and is parallel to the given line.

Answer to Problem 14Q

The required equation of the line is $y=-4x-16$ .

Explanation of Solution

Given:

The given graph is shown in Figure 1

  

Figure 1

Calculation:

Consider the slope of the line is given by the equation.

  $m=\frac{y_2-y_1}{x_2-x_1}$

For the line to be parallel to the given line the slopes must be equal.

The slope of the line here is $m=-4$ . Then, by the point slope form,

  $\begin{array}{l}-4=\frac{y-0}{x-\left(-4\right)}\\ y=-4x-16\end{array}$

(b)

To determine

To find: The equation for the line that passes through the given point and is parallel to the given line.

Answer to Problem 14Q

The required equation of the line is $y=\frac{1}{4}x+1$ .

Explanation of Solution

Given:

The given graph is shown in Figure 1

  

Figure 2

Calculation:

Consider the slope of the line is given by the equation.

  $m=\frac{y_2-y_1}{x_2-x_1}$

For the line to be perpendicular to the given line the slopes must be negative reciprocal of each other.

The slope of the line here is $\frac{1}{4}$ . Then, by the point slope form,

  $\begin{array}{l}\frac{1}{4}=\frac{y-0}{x-\left(-4\right)}\\ y=\frac{1}{4}x+1\end{array}$