Line \( t \) passes through points \( (10,4) \) and \( (1,2) \). Line \( u \) is perpendicular to \( t \). What is the slope of line \( u \) ? Simplify your answer and write it as a proper fraction, improper fraction, or integer.

To find the slope of line \( t \), we can use the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\): \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \] Here, the points are \((10, 4)\) and \((1, 2)\). Plugging in these values: \[ \text{slope of } t = \frac{2 - 4}{1 - 10} = \frac{-2}{-9} = \frac{2}{9} \] Since line \( u \) is perpendicular to line \( t \), its slope will be the negative reciprocal of the slope of line \( t \): \[ \text{slope of } u = -\frac{1}{\text{slope of } t} = -\frac{1}{\frac{2}{9}} = -\frac{9}{2} \] Thus, the slope of line \( u \) is \[ \boxed{-\frac{9}{2}}. \]