To find the slope of the line passing through the points \((6, -1)\) and \((7, 3)\), we'll start by identifying the coordinates:
- \((x_1, y_1) = (6, -1)\)
- \((x_2, y_2) = (7, 3)\)
Now we can fill in the slope formula:
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the values into the formula:
- \(y_1 = -1\)
- \(y_2 = 3\)
- \(x_1 = 6\)
- \(x_2 = 7\)
Now, we can compute it step by step:
- Calculate \(y_2 - y_1\):
\[ y_2 - y_1 = 3 - (-1) = 3 + 1 = 4 \]
- Calculate \(x_2 - x_1\):
\[ x_2 - x_1 = 7 - 6 = 1 \]
- Substitute these values into the slope formula:
\[ \text{slope} = \frac{4}{1} \]
- Simplify:
\[ \text{slope} = 4 \]
Thus, the slope of the line passing through the points \((6, -1)\) and \((7, 3)\) is \(4\).