$$ (-1,3) ;(5,-5) $$ What is the slope of the line containing the points $$ (-1,3) $$ and $$ (5,-5) $$ ? Seleot the correct choice below and fill in any answer boxes within your choice. A. The slope is $$ \square $$, Graph the line. B. The slope is undefined. B. The line containing the given points.

Question

UpStudy AI · Accepted Answer

To find the slope of the line containing the points $$ (-1, 3) $$ and $$ (5, -5) $$, we'll use the slope formula:

$$
\text{Slope } (m) = \frac{y_2 - y_1}{x_2 - x_1}
$$

**Given Points:**
- $$ (x_1, y_1) = (-1, 3) $$
- $$ (x_2, y_2) = (5, -5) $$

**Calculating the Slope:**
$$
m = \frac{-5 - 3}{5 - (-1)} = \frac{-8}{6} = -\frac{4}{3}
$$

**Correct Choice:**

**A. The slope is $$ -\frac{4}{3} $$, Graph the line.**

---

### Graphing the Line

To graph the line with a slope of $$ -\frac{4}{3} $$ passing through the points $$ (-1, 3) $$ and $$ (5, -5) $$:

1. **Plot the Given Points:**
   - Plot $$ (-1, 3) $$ and $$ (5, -5) $$ on the coordinate plane.

2. **Use the Slope to Find Another Point:**
   - Starting from $$ (-1, 3) $$, move 3 units to the right (positive $$ x $$-direction) and 4 units down (negative $$ y $$-direction) to reach the next point.
   - This brings you to $$ (2, -1) $$.

3. **Draw the Line:**
   - Connect the points $$ (-1, 3) $$, $$ (2, -1) $$, and $$ (5, -5) $$ with a straight line.

4. **Extend the Line:**
   - Continue the line in both directions beyond the plotted points for a complete graph.

**Graph Example:**

```
y
|
7 |           
6 |         
5 |         
4 |         
3 |    * (-1,3)
2 |         
1 |         
0 |-------------------------- x
-1|            * (2,-1)
-2|
-3|
-4|
-5|                 * (5,-5)
|
```

*Note: The above is a simplified representation. For an accurate graph, use graphing paper or a digital graphing tool.*
The slope of the line is $$ -\frac{4}{3} $$.

\[ (-1,3) ;(5,-5) \] What is the slope of the line containing the points \( (-1,3) \) and \( (5,-5) \) ? Seleot the correct choice below and fill in any answer boxes within your choice. A. The slope is \( \square \), Graph the line. B. The slope is undefined. B. The line containing the given points.

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