To find the slope of the line that passes through the points \( (5, 10) \) and \( (7, 12) \), we can use the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, \( (x_1, y_1) = (5, 10) \) and \( (x_2, y_2) = (7, 12) \).
Substituting the values:
\[ m = \frac{12 - 10}{7 - 5} = \frac{2}{2} = 1 \]
Thus, the slope of the line is:
\[ \text{Slope} = 1 \]