Pregunta
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
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The slope is undefined.
Solución
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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Como
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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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