To find the slope between the points \((5, 1)\) and \((10, 8)\), we can use the slope formula:
\[ \text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, \((x_1, y_1) = (5, 1)\) and \((x_2, y_2) = (10, 8)\).
Now, substitute the values into the formula:
\[ m = \frac{8 - 1}{10 - 5} = \frac{7}{5} \]
So, the slope between the points \((5, 1)\) and \((10, 8)\) is \(\frac{7}{5}\).