What is the slope of the line throught (-3,7) and (2,5) in the standard (x, y) coordiante plane ?

Options

A. `-5/2`
B. `-2/5`
C. underfined
D. `2/5`

Answer

To find the slope of the line that passes through the points (-3, 7) and (2, 5), we can use the slope formula:

\[ \text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1} \]

### Step-by-step Solution:

1. **Identify the Points:**
- Let the first point be \( (x_1, y_1) = (-3, 7) \)
- Let the second point be \( (x_2, y_2) = (2, 5) \)

2. **Substitute the Values into the Slope Formula:**
- Using the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substitute \( y_2 = 5 \), \( y_1 = 7 \), \( x_2 = 2 \), and \( x_1 = -3 \):
\[ m = \frac{5 - 7}{2 - (-3)} \]

3. **Calculate the Differences:**
- Calculate \( y_2 - y_1 \):
\[ 5 - 7 = -2 \]
- Calculate \( x_2 - x_1 \):
\[ 2 - (-3) = 2 + 3 = 5 \]

4. **Substitute the Differences Back into the Formula:**
\[ m = \frac{-2}{5} \]

5. **Final Result:**
- The slope of the line is:
\[ m = -\frac{2}{5} \]

### Final Answer:
The slope of the line through the points (-3, 7) and (2, 5) is \( -\frac{2}{5} \).

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