find the slope of the line passing through the points (-2, -7) and (3, 5).

Explanation:

Step1: Recall the slope formula

The slope formula is (m=\frac{y_2 - y_1}{x_2 - x_1}). Let ((x_1,y_1)=(-2,-7)) and ((x_2,y_2)=(3,5)).

Step2: Substitute the values into the formula

Substitute (x_1=-2,y_1 = - 7,x_2=3,y_2=5) into (m=\frac{y_2 - y_1}{x_2 - x_1}), we get (m=\frac{5-(-7)}{3-(-2)}).

Step3: Simplify the numerator and denominator

Simplify the numerator: (5-(-7)=5 + 7=12). Simplify the denominator: (3-(-2)=3 + 2=5). So (m=\frac{12}{5}).

Answer:

(\frac{12}{5})