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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, their slopes are negative reciprocals of each other. This means that the slope of one line is the negative inverse (-1/m) of the slope of the other line.

Step by step solution

01

Understand the Concept of Slope

Slope refers to the incline of a line, the steepness or the angle it forms with the horizontal axis. In mathematics, the slope of a line is generally represented by the letter 'm' and could be defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line (i.e., m = rise/run).
02

Learn the Relationship between Slopes of Perpendicular Lines

If two lines are perpendicular, their slopes are negative reciprocals of each other. This means that if the slope of line A is m, then the slope of line B (perpendicular to A) is -1/m. So, for two lines with slopes m1 and m2, if the lines are perpendicular, then m1*m2 = -1.
03

Example of Perpendicular Lines

For example, consider two lines such that line A is y = 3x + 2 and line B is y = -1/3x + 4. The slope of line A is 3 and the slope of line B is -1/3. As you can see, these two slopes are negative reciprocals of each other. Thus these lines are perpendicular.

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