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Chapter 2: Problem 32

If two lines are perpendicular, describe the relationship between their slopes.

Short Answer

Expert verified
If two lines are perpendicular, then the product of their slopes is -1. Therefore, the slope of one line is the negative reciprocal of the slope of the other line.

Step by step solution

01

Understand Perpendicular lines

Perpendicular lines are two lines that intersect at a right angle (90 degrees). This characteristic is significant in understanding the relationship between the slopes of the lines.
02

Derive slope of a line

The slope of a line in a two-dimensional Cartesian coordinate system is found by the equation \(m = \frac{y_2 - y_1}{x_2 - x_1}\), where \(x_1, y_1\) and \(x_2, y_2\) are the coordinates of two points on the line, and \(m\) is the slope.
03

Relationship between the slopes of perpendicular lines

If two lines are perpendicular, the product of their slopes equals -1. This means that the slope of one line is the negative reciprocal of the slope of the other line.

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