Chapter 5.6, Problem 7P

Determine whether the graphs of the given equations are parallel, perpendicular, or neither. Explain.

$y=4x+5$

$-4x+y=-13$

To determine

Whether the graphs of $y=4x+5\text{and}-4x+y=-13$ are parallel, perpendicular, or neither.

Answer to Problem 7P

Both the given equations have the same slope, $4$ . Therefore, the graphs of these equations are parallel.

Explanation of Solution

Given information:

The equations are

  $\begin{array}{l}y=4x+5\\ -4x+y=-13\end{array}$

Writing the given equations in slope-intercept form as follows:

  $\begin{array}{l}y=4x+5\\ -4x+y=-13\Rightarrow y=4x-13\end{array}$

Conclusion:

Since both the given equations have the same slope, $4$ , the graphs of these equations are parallel.