find the slope of the line passing through the points (2,5) and (8, - 4).

Explanation:

Step1: Identify the coordinates

Let ((x_1,y_1)=(2,5)) and ((x_2,y_2)=(8, - 4))

Step2: Use the slope formula

The slope formula is (m=\frac{y_2 - y_1}{x_2 - x_1}). Substitute the values: (m=\frac{-4 - 5}{8 - 2})

Step3: Calculate the numerator and denominator

(-4-5=-9), (8 - 2=6) So (m=\frac{-9}{6})

Step4: Simplify the fraction

Divide numerator and denominator by 3: (\frac{-9\div3}{6\div3}=\frac{-3}{2})

Answer:

(\frac{-3}{2})