Problem 32
Question
If two lines are perpendicular, describe the relationship between their slopes.
Step-by-Step Solution
Verified Answer
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.
1Step 1: 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).
2Step 2: 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.
3Step 3: 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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Problem 32
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