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. \( (6,-9) \) and \( (-9,-9) \) Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The slope is OB. The slope is undefined.
Ask by Frank Owen. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The slope is 0, and the line is horizontal.
Solution
To determine the slope of the line passing through the points \( (6, -9) \) and \( (-9, -9) \), follow these steps:
1. **Calculate the Change in \( y \) (Δy):**
\[
\Delta y = y_2 - y_1 = -9 - (-9) = 0
\]
2. **Calculate the Change in \( x \) (Δx):**
\[
\Delta x = x_2 - x_1 = -9 - 6 = -15
\]
3. **Determine the Slope (m):**
\[
m = \frac{\Delta y}{\Delta x} = \frac{0}{-15} = 0
\]
Since the slope \( m = 0 \), the line is **horizontal**.
**Answer:**
**A. The slope is 0. The line is horizontal.**
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Simplify this solution The Deep Dive
To find the slope of the line through the points \( (6, -9) \) and \( (-9, -9) \), we use the slope formula: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-9 - (-9)}{-9 - 6} = \frac{0}{-15} = 0. \] Since the slope is 0, this indicates that the line is horizontal. So, the correct choice is: A. The slope is 0, and the line is horizontal. Now, imagine this line stretching across a flat field, perfectly level, like laying out a picnic blanket on a calm day—absolutely no hills or valleys in sight!
