Find the slope of the line passing through the points \( (-4,-3) \) and \( (8,-9) \).

To find the slope of a line passing through two points, you can use the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] For the points \( (-4,-3) \) and \( (8,-9) \), let’s identify \( (x_1, y_1) = (-4, -3) \) and \( (x_2, y_2) = (8, -9) \). Substituting these values into the formula: \[ m = \frac{-9 - (-3)}{8 - (-4)} = \frac{-9 + 3}{8 + 4} = \frac{-6}{12} = -\frac{1}{2} \] So, the slope of the line is \( -\frac{1}{2} \). Now let’s add a couple of fun facts! Did you know that the concept of slope comes from geometry? It was historically developed to measure the steepness of lines on a graph, and the idea has roots going back to ancient Greek mathematics! Also, in real-world applications, the slope can represent various scenarios. For instance, in finance, if you were plotting your spending vs. time, a negative slope might indicate you're saving money over time, while a positive slope would suggest you're spending more!