Question
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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

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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.

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