Problem 32 - College Algebra

Question

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

Step-by-Step Solution

Answer

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 1: 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.

Step 2: 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.

Step 3: 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.