The tangent line to the graph of function \( f \) at the point \( (2,3) \) passes through.the point \( (7,6) \). Find \( f^{\prime}(2) \). \( f^{\prime}(2)= \)

To find \( f^{\prime}(2) \), we need to determine the slope of the tangent line to the function \( f \) at the point \( (2, 3) \). The slope of the tangent line can be calculated using the two points that lie on the line: \( (2, 3) \) and \( (7, 6) \). The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] In our case, we can let \( (x_1, y_1) = (2, 3) \) and \( (x_2, y_2) = (7, 6) \). Plugging in these values, we get: \[ m = \frac{6 - 3}{7 - 2} = \frac{3}{5} \] Since the slope of the tangent line at the point \( (2, 3) \) is equal to the derivative \( f^{\prime}(2) \), we have: \[ f^{\prime}(2) = \frac{3}{5} \] Thus, the value of \( f^{\prime}(2) \) is \[ \boxed{\frac{3}{5}} \]