The slope of a line is -3. Find the slope of a line that is perpendicular to this line.
A. -3
B. -1/3
C. 1/3
Answer (1)
The problem provides the slope of a line as -3 and asks for the slope of a line perpendicular to it.
Recall that the slopes of perpendicular lines are negative reciprocals of each other.
Calculate the negative reciprocal of -3: − − 3 1 = 3 1 .
The slope of the perpendicular line is 3 1 .
Explanation
Understanding Perpendicular Slopes The problem states that the slope of a line is -3, and we need to find the slope of a line that is perpendicular to it. Recall that two lines are perpendicular if and only if the product of their slopes is -1. This means that if a line has slope m , a line perpendicular to it has slope − m 1 .
Calculating the Perpendicular Slope Given the slope of the line is m 1 = − 3 , we need to find the slope of the perpendicular line, m 2 . Using the formula for perpendicular slopes, we have: m 2 = − m 1 1 = − − 3 1 = 3 1 Thus, the slope of the line perpendicular to the given line is 3 1 .
Final Answer Therefore, the slope of a line perpendicular to a line with slope -3 is 3 1 .
Examples
Imagine you're designing a rectangular garden. One side of the garden has a slope of -3. To ensure the adjacent side is perfectly perpendicular, you need to calculate its slope. Using the principle that perpendicular lines have slopes that are negative reciprocals of each other, you determine the slope of the adjacent side should be 3 1 . This ensures your garden has perfect right angles at the corners, making it aesthetically pleasing and structurally sound.
