Question

a line intersects the points (3, 6) and (5, -4). 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 \( m = \frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify coordinates

Let \((x_1, y_1) = (3, 6)\) and \((x_2, y_2) = (5, -4)\).

Step3: Substitute into formula

Substitute values: \( m = \frac{-4 - 6}{5 - 3} \).

Step4: Simplify numerator and denominator

Calculate numerator: \(-4 - 6 = -10\). Denominator: \(5 - 3 = 2\). So \( m = \frac{-10}{2} = -5 \).

Answer:

\(-5\)