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.
and
Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. The slope is 0 . (Simplify your answer.)
B. The slope is undefined.
Andicate whether the line through the points rises, falls, is horizontal, or is vertical.
B. The line is horizontal.
C. The line rises from left to right.
D. The line falls from left to right.

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.

and

Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. The slope is 0 . (Simplify your answer.)
B. The slope is undefined.
Andicate whether the line through the points rises, falls, is horizontal, or is vertical.
B. The line is horizontal.
C. The line rises from left to right.
D. The line falls from left to right.

UpStudy AI · Accepted Answer

To determine the slope of the line passing through the points $$(-2, 3)$$ and $$ (8, 3) $$, follow these steps:

1. **Calculate the Slope ($$m$$):**
   
   The formula for the slope between two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ is:
   $$
   m = \frac{y_2 - y_1}{x_2 - x_1}
   $$
   
   Plugging in the given points:
   $$
   m = \frac{3 - 3}{8 - (-2)} = \frac{0}{10} = 0
   $$

2. **Determine the Nature of the Line:**
   
   - **Slope Interpretation:**
     - If $$m = 0$$, the line is **horizontal** because there is no change in the $$y$$-coordinates as $$x$$ changes.
     - If the slope were undefined (division by zero), the line would be **vertical**.
     - A positive slope indicates the line **rises** from left to right.
     - A negative slope indicates the line **falls** from left to right.

- **In this case:**
     - Since $$m = 0$$, the line is **horizontal**.

**Final Answer:**

**A. The slope is $$0$$.**

**B. The line is horizontal.**
The slope is 0, and the line is horizontal.

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