Find the slope of a line parallel to the which passes through the following points:
(-1, 3) and (4, 7)

Answer

To find the slope of a line parallel to the one that passes through the points (-1, 3) and (4, 7), we first need to calculate the slope of the line that connects these two points.

### Step-by-Step Solution:

1. **Identify the Points:**
We have two points:
- Point 1: \((x_1, y_1) = (-1, 3)\)
- Point 2: \((x_2, y_2) = (4, 7)\)

2. **Use the Slope Formula:**
The formula for the slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

3. **Substitute the Values:**
Substitute the coordinates of the points into the slope formula:
\[ m = \frac{7 - 3}{4 - (-1)} \]

4. **Calculate the Differences:**
Simplifying the numerator and the denominator:
- Numerator: \(7 - 3 = 4\)
- Denominator: \(4 - (-1) = 4 + 1 = 5\)

5. **Calculate the Slope:**
Now substitute these values back into the slope formula:
\[ m = \frac{4}{5} \]

6. **Identify the Slope of the Parallel Line:**
Since parallel lines have the same slope, the slope of the line parallel to the one that passes through the points (-1, 3) and (4, 7) is also:
\[ m = \frac{4}{5} \]

### Final Answer:
The slope of the line parallel to the one that passes through the points (-1, 3) and (4, 7) is \(\frac{4}{5}\).