What is the slope of a line perpendicular to y = x + 5? O A. 3 о в. 1 ос. 4 O D. 3

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
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**Mathematics Quiz: Understanding Slopes of Perpendicular Lines**

**Question:**

What is the slope of a line perpendicular to \( y = \frac{3}{4}x + 5 \)?

**Options:**

- **A.** \( -\frac{3}{4} \)
- **B.** \( \frac{1}{5} \)
- **C.** \( \frac{4}{3} \)
- **D.** \( -\frac{4}{3} \)

**Explanation:**

To determine the slope of a line that is perpendicular to another line, you need to take the negative reciprocal of the original line's slope. The given equation is \( y = \frac{3}{4} x + 5 \), which has a slope of \( \frac{3}{4} \).

The negative reciprocal of \( \frac{3}{4} \) is \( -\frac{4}{3} \).

Therefore, the slope of a line perpendicular to \( y = \frac{3}{4}x + 5 \) is:

**Answer: D. \( -\frac{4}{3} \)**
Transcribed Image Text:**Mathematics Quiz: Understanding Slopes of Perpendicular Lines** **Question:** What is the slope of a line perpendicular to \( y = \frac{3}{4}x + 5 \)? **Options:** - **A.** \( -\frac{3}{4} \) - **B.** \( \frac{1}{5} \) - **C.** \( \frac{4}{3} \) - **D.** \( -\frac{4}{3} \) **Explanation:** To determine the slope of a line that is perpendicular to another line, you need to take the negative reciprocal of the original line's slope. The given equation is \( y = \frac{3}{4} x + 5 \), which has a slope of \( \frac{3}{4} \). The negative reciprocal of \( \frac{3}{4} \) is \( -\frac{4}{3} \). Therefore, the slope of a line perpendicular to \( y = \frac{3}{4}x + 5 \) is: **Answer: D. \( -\frac{4}{3} \)**
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