Chapter 13.7, Problem 23PSC

To determine

To find: The distance between the lines for the given equation.

Answer to Problem 23PSC

The required distance between the two lines is $\frac{8}{\sqrt{5}}$ .

Explanation of Solution

Given:

The equations are,

  $\begin{array}{l}y=2x-1\\ y=2x+7\end{array}$

Calculation:

Consider the graph for the given equations is shown in Figure 1

  

Figure 1

Consider the formula for the distance between the two parallel lines is,

  $\begin{array}{c}d=\frac{\left|c_1+c_2\right|}{\sqrt{1+m^2}}\\ =\left|\frac{-1-7}{\sqrt{1+2^2}}\right|\\ =\frac{8}{\sqrt{5}}\end{array}$