If a line has a slope of $3$, which of the following lines is perpendicular to it?

• A. A line with slope $1$
• B. A line with slope $3$
• C. A line with slope $-3$
• D. A line with slope $-\frac{1}{3}$

Answer: (D)

Verified step by step guidance

1. Recall that two lines are perpendicular if the product of their slopes is -1. This means if one line has slope \(m\), the slope of a line perpendicular to it is \(-\frac{1}{m}\).
2. Given the slope of the first line is 3, identify the slope of the perpendicular line by calculating \(-\frac{1}{3}\).
3. Check each given slope option to see which one matches \(-\frac{1}{3}\):
4. - Slope 1: The product with 3 is \$3 \times 1 = 3$, not -1.
5. - Slope 3: The product with 3 is \$3 \times 3 = 9$, not -1.
6. - Slope -3: The product with 3 is \$3 \times (-3) = -9$, not -1.
7. - Slope \(-\frac{1}{3}\): The product with 3 is \$3 \times (-\frac{1}{3}) = -1$, which satisfies the condition for perpendicularity.