Find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line. Containing the points \( (3,6) \) and \( (5,5) \) The equation is (Type an equation. Simplify your answer.)

To find the equation of the line containing the points \( (3,6) \) and \( (5,5) \), we first need to calculate the slope \( m \). The formula for the slope between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Plugging in our points: \[ m = \frac{5 - 6}{5 - 3} = \frac{-1}{2} \] Now, we can use the point-slope form \( y - y_1 = m(x - x_1) \). Using point \( (3, 6) \): \[ y - 6 = -\frac{1}{2}(x - 3) \] Distributing and simplifying gives: \[ y - 6 = -\frac{1}{2}x + \frac{3}{2} \] \[ y = -\frac{1}{2}x + \frac{3}{2} + 6 \] \[ y = -\frac{1}{2}x + \frac{15}{2} \] So, the equation of the line in slope-intercept form is: \[ y = -\frac{1}{2}x + \frac{15}{2} \]