13 Identify the slope of a line that passes through \( (1,5) \) and \( (5,-4) \)

\[ \textbf{Step 1: Identify the slope formula} \] The formula for the slope \( m \) of a line is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] \[ \textbf{Step 2: Substitute the given points into the formula} \] Given the points \( (1, 5) \) and \( (5, -4) \), let: \[ (x_1, y_1) = (1, 5) \quad \text{and} \quad (x_2, y_2) = (5, -4) \] Substitute these values into the formula: \[ m = \frac{-4 - 5}{5 - 1} \] \[ \textbf{Step 3: Simplify the numerator and the denominator} \] Calculate the numerator: \[ -4 - 5 = -9 \] Calculate the denominator: \[ 5 - 1 = 4 \] Thus: \[ m = \frac{-9}{4} \] \[ \textbf{Step 4: Conclude the result} \] The slope of the line is: \[ m = -\frac{9}{4} \]