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Chapter 1: Problem 145

Is it possible for two lines with positive slopes to be perpendicular? Explain.

Short Answer

Expert verified
No, two lines with positive slopes cannot be perpendicular because the product of their slopes is not -1.

Step by step solution

01

Understanding the concept of Slope

The slope of a line in a plane is the measure of the vertical change (rise) for each unit of horizontal change (run). A positive slope means the line rises as it moves to the right, while a negative slope means the line declines.
02

Understanding Perpendicular Lines and their slopes

Perpendicular lines are two lines that intersect at a right angle. In a Cartesian coordinate system, if two lines are perpendicular, the product of their slopes is -1. More simply put, the slopes of two perpendicular lines are negative reciprocals of each other.
03

Assessing if two lines with positive slopes can be perpendicular

The key is knowing that the slopes of two perpendicular lines are negative reciprocals. If both lines had positive slopes (say m and n), their product would also be positive (since a positive number times a positive number is positive). However, we know that the product of the slopes of two perpendicular lines should be -1, which is negative. Therefore, it becomes clear that two lines with positive slopes cannot be perpendicular.

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