Chapter 13, Problem 30RP

To determine

To find: The distance between the graph of the given equation.

Answer to Problem 30RP

Thedistance between the two lines is $\sqrt{10}$ .

Explanation of Solution

Given:

The given equations are $y=3x-8$ and $y=3x-2$ .

Calculation:

The given equations are,

  $\begin{array}{l}y=3x-8\\ y=3x-2\end{array}$

Consider the graph of the given equation is shown in Figure 1

  

Figure 1

The graph shows that the lines are parallel. Then the perpendicular distance between the two lines is obtained as,

  $d=\frac{\left|c_1-c_2\right|}{\sqrt{A^2-B^2}}$

Here, the coefficients are $A$ and B of $x$ and $y$ respectively and $c_1,c_2$ are the intercepts.

  $\begin{array}{c}d=\frac{\left|2-\left(-8\right)\right|}{\sqrt{3^2+1^2}}\\ =\sqrt{10}\end{array}$