Question

find the slope of the line passing through the points (-5, -2) and (3, -9).

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
Let \( (x_1, y_1) = (-5, -2) \) and \( (x_2, y_2) = (3, -9) \).

Step2: Substitute values

Substitute into the formula: \( m = \frac{-9 - (-2)}{3 - (-5)} \).

Step3: Simplify numerator and denominator

Simplify numerator: \( -9 - (-2) = -9 + 2 = -7 \).
Simplify denominator: \( 3 - (-5) = 3 + 5 = 8 \).

Step4: Get slope

So, \( m = \frac{-7}{8} \).

Answer:

\( -\frac{7}{8} \)