Chapter 5.6, Problem 8P

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

$y=\frac{7}{9}x-7$

$y=-\frac{7}{9}x+3$

To determine

To find: Whether the provided equations are perpendicular, parallel or neither.

Answer to Problem 8P

The equations are perpendicular.

Explanation of Solution

Given:

The equation is:

  $\begin{array}{l}y=\frac{7}{9}x-7\\ y=-\frac{7}{9}x+3\end{array}$

Concept used:

Two equations are said to be perpendicular if their slopes are not equal.

Calculation:

The slope of the line $y=\frac{7}{9}x-7$ is $\frac{7}{9}$

Similarly,

The slope of the line $y=-\frac{7}{9}x+3$ is $-\frac{7}{9}$

Since, the slope of the two lines are opposite of each other. Thus, it could be said that these two lines are perpendicular.