find the slope of the line passing through the points (3,4) and (8, - 3).

Explanation:

Step1: Identify the formula for slope

The formula for the slope (m) between two points ((x_1,y_1)) and ((x_2,y_2)) is (m=\frac{y_2 - y_1}{x_2 - x_1}).

Step2: Assign values to (x_1,y_1,x_2,y_2)

Let ((x_1,y_1)=(3,4)) and ((x_2,y_2)=(8, - 3)). Then (y_2=-3,y_1 = 4,x_2=8,x_1=3).

Step3: Substitute values into the formula

(m=\frac{-3 - 4}{8 - 3}).

Step4: Simplify the numerator and denominator

The numerator: (-3-4=-7). The denominator: (8 - 3=5). So (m=\frac{-7}{5}).

Answer:

(\frac{-7}{5})