a line intersects the points (-2, 9) and (3, -11). what is the slope of this line in simplest form? m = ?

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. Let ((x_1,y_1)=(-2,9)) and ((x_2,y_2)=(3,-11)).

Step2: Substitute the values into the formula

Substitute (x_1=-2,y_1 = 9,x_2=3,y_2=-11) into (m=\frac{y_2 - y_1}{x_2 - x_1}), we get (m=\frac{-11 - 9}{3-(-2)}).

Step3: Simplify the numerator and denominator

First, simplify the numerator: (-11-9=-20). Then simplify the denominator: (3-(-2)=3 + 2=5). So (m=\frac{-20}{5}).

Step4: Calculate the final value

(\frac{-20}{5}=-4).

Answer:

(-4)