Question

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

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Let \((x_1, y_1)=(-2, 9)\) and \((x_2, y_2)=(3, -11)\).

Step2: Substitute values into formula

Substitute \( x_1=-2 \), \( y_1 = 9 \), \( x_2=3 \), \( y_2=-11 \) into the slope formula:
\( m=\frac{-11 - 9}{3 - (-2)} \)

Step3: Simplify numerator and denominator

Simplify the numerator: \(-11 - 9=-20\)
Simplify the denominator: \(3 - (-2)=3 + 2 = 5\)

Step4: Calculate the slope

Now, \( m=\frac{-20}{5}=-4 \)

Answer:

\(-4\)