Chapter 5.6, Problem 12P

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

$y=4x+12$

$x+4y=32$

To determine

Whether the graphs of $y=4x+12\text{and}x+4y=32$ are parallel, perpendicular, or neither.

Answer to Problem 12P

The product of the slopes of given equations is $-1$ . Therefore, the graphs of these equations are perpendicular.

Explanation of Solution

Given information:

The equations are

  $\begin{array}{l}y=4x+12\\ x+4y=32\end{array}$

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

  $\begin{array}{l}y=4x+12\\ x+4y=32\Rightarrow y=-\frac{1}{4}x+8\end{array}$

The slope of the first equation is $4$ and that of the second equation is $-\frac{1}{4}$ . So their product would be

  $4\times -\frac{1}{4}=-1$ .

Conclusion:

Since the product of the slopes of given equations is $-1$ , the graphs of these equations are perpendicular.