Question
Find the slope, if it exists. \( x=-6 \) Select the correct choice below and fill in any answer boxes within your choice. A. The slope of the line is \( \mathrm{m}=\square \). (Type an integer or a simplified fraction.) B. The slope is undefined.
Ask by Lewis Garrett. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The slope is undefined.
Solution
The equation \( x = -6 \) represents a vertical line.
1. **Understanding the slope of a vertical line:**
- The slope of a line is defined as the change in \( y \) divided by the change in \( x \) (i.e., \( m = \frac{\Delta y}{\Delta x} \)).
- For a vertical line, the change in \( x \) is always zero (since \( x \) does not change), which leads to division by zero in the slope formula.
2. **Conclusion:**
- Since division by zero is undefined, the slope of a vertical line is also undefined.
Thus, the correct choice is:
B. The slope is undefined.
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Beyond the Answer
In the case of the line given by the equation \( x = -6 \), this represents a vertical line. Vertical lines have no defined slope because the ratio of the change in \( y \) to the change in \( x \) is undefined—specifically, the change in \( x \) is 0, leading to division by zero. Therefore, the slope is undefined. B. The slope is undefined.