Find the slope of the line passing through the given pair of points, if the slope is defined. Answer exactly. \( \left(\frac{1}{2}, \frac{1}{2}\right) \) and \( \left(-\frac{1}{4},-2\right) \)

To find the slope of the line passing through the points \( \left(\frac{1}{2}, \frac{1}{2}\right) \) and \( \left(-\frac{1}{4}, -2\right) \), we use the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Plugging in the coordinates \( (x_1, y_1) = \left(\frac{1}{2}, \frac{1}{2}\right) \) and \( (x_2, y_2) = \left(-\frac{1}{4}, -2\right) \): \[ m = \frac{-2 - \frac{1}{2}}{-\frac{1}{4} - \frac{1}{2}} \] Calculating the differences: Numerator: \[ -2 - \frac{1}{2} = -\frac{4}{2} - \frac{1}{2} = -\frac{5}{2} \] Denominator: \[ -\frac{1}{4} - \frac{1}{2} = -\frac{1}{4} - \frac{2}{4} = -\frac{3}{4} \] Now substituting back into the slope formula: \[ m = \frac{-\frac{5}{2}}{-\frac{3}{4}} = \frac{-5}{2} \cdot \frac{-4}{3} = \frac{20}{6} = \frac{10}{3} \] So, the slope of the line is \( \frac{10}{3} \).