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

Explanation:

Step1: Recall the slope formula

The slope formula is (m=\frac{y_2 - y_1}{x_2 - x_1}), where ((x_1,y_1)) and ((x_2,y_2)) are two points on the line.

Step2: Identify the coordinates

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

Step3: Substitute into the formula

Substitute (x_1 = 2,y_1 = 5,x_2 = 8,y_2=-4) into (m=\frac{y_2 - y_1}{x_2 - x_1}), we get (m=\frac{-4 - 5}{8 - 2}).

Step4: Calculate the numerator and denominator

First, calculate the numerator: (-4-5=-9). Then calculate the denominator: (8 - 2=6). So (m=\frac{-9}{6}).

Step5: Simplify the fraction

Simplify (\frac{-9}{6}) by dividing both the numerator and denominator by 3. We get (m =-\frac{3}{2}).

Answer:

(-\frac{3}{2})