Question
Find the slope of the line passing through the pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. \( (-9,-4) \) and \( (-9,9) \) Select the correct choice below and fill in the answer box within your choice. A. The slope is B. The slope is undefined.
Ask by Simpson Smith. in the United States
Jan 25,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The slope is undefined, and the line is vertical.
Solution
**B. The slope is undefined.**
The line through the points \( (-9, -4) \) and \( (-9, 9) \) is **vertical**.
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**Explanation:**
- Both points have the same \( x \)-coordinate (\( x = -9 \)), which means the line is vertical.
- A vertical line does not have a defined slope because the change in \( x \) is zero, leading to division by zero when calculating the slope.
- Therefore, the slope is **undefined**, and the line is **vertical**.
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Simplify this solution Beyond the Answer
The slope of the line passing through the points \((-9,-4)\) and \((-9,9)\) is undefined. This is because both points have the same x-coordinate (-9), which means the line formed by these points is vertical. Vertical lines don't have a defined slope since the change in x (denominator) is zero, leading to a division by zero scenario. So, the choice is B. The slope is undefined. The line through these points is vertical!
