In a coordinate plane, if line A has a slope of 3 and line B is perpendicular to

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Question: In a coordinate plane, if line A has a slope of 3 and line B is perpendicular to line A, what is the slope of line B?

Options:

Correct Answer: -1/3

Solution:

The slope of a line perpendicular to another is the negative reciprocal. Therefore, the slope of line B is -1/3.

In a coordinate plane, if line A has a slope of 3 and line B is perpendicular to line A, what is the slope of line B?

In a coordinate plane, if line A has a slope of 3 and line B is perpendicular to line A, what is the slope of line B?

Step 1: Understand that the slope of line A is given as 3.
Step 2: Know that when two lines are perpendicular, their slopes have a special relationship.
Step 3: The relationship is that the slope of one line is the negative reciprocal of the other line's slope.
Step 4: To find the negative reciprocal of a slope, first take the reciprocal (which means flipping the fraction).
Step 5: The reciprocal of 3 is 1/3.
Step 6: Now, make it negative. So, the negative reciprocal of 3 is -1/3.
Step 7: Therefore, the slope of line B, which is perpendicular to line A, is -1/3.

Slope of a Line – The slope of a line in a coordinate plane represents its steepness and direction, calculated as the rise over run.
Perpendicular Lines – Two lines are perpendicular if the product of their slopes is -1, meaning the slope of one line is the negative reciprocal of the other.