Chapter 5.6, Problem 13P

Determine whether each statement is always, sometimes, or never true. Explain.

Two lines with different slopes are perpendicular.

To determine

Whether the statement “Two lines with different slopes are perpendicular.” is always , sometimes , or never true.

Answer to Problem 13P

When two lines are having different slopes, then there is a possibility of lines being perpendicular when the product of the slopes is $-1$ . Suppose if the slopes are different and their product is not $-1$ , then the lines need not to be perpendicular. Therefore, the given statement is sometimes true.

Explanation of Solution

Given information:

The statement is “Two lines with different slopes are perpendicular.”

When two lines are having different slopes, then there is a possibility of lines being perpendicular when the product of the slopes is $-1$ . Suppose if the slopes are different and their product is not $-1$ , then the lines need not to be perpendicular.

Conclusion:

Therefore, the given statement is sometimes true.