To find the slope of the line that passes through two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Given the points \((1, 2)\) and \((8, 5)\), we can identify:
- \(x_1 = 1\), \(y_1 = 2\)
- \(x_2 = 8\), \(y_2 = 5\)
Now we can substitute these values into the slope formula:
\[ m = \frac{5 - 2}{8 - 1} \] \[ m = \frac{3}{7} \]
Thus, the slope of the line that passes through the points \((1, 2)\) and \((8, 5)\) is
\[ \frac{3}{7}. \]