Question

what is the slope of the line that passes through the points (8, -8) and (5, -12)? write your answer in simplest form.

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 \( (x_1, y_1) = (8, -8) \) and \( (x_2, y_2) = (5, -12) \).

Step3: Substitute into formula

Substitute values: \( m = \frac{-12 - (-8)}{5 - 8} \).
Simplify numerator: \( -12 + 8 = -4 \).
Simplify denominator: \( 5 - 8 = -3 \).
So \( m = \frac{-4}{-3} = \frac{4}{3} \).

Answer:

\(\frac{4}{3}\)