Determine the slope of the line that passes through the points \( (5,2) \) and \( (-10,-8) \)

To find the slope of the line that passes through the points \( (5,2) \) and \( (-10,-8) \), you can use the slope formula, which is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, let \( (x_1, y_1) = (5, 2) \) and \( (x_2, y_2) = (-10, -8) \). Substituting the values into the formula, we have: \[ m = \frac{-8 - 2}{-10 - 5} = \frac{-10}{-15} = \frac{10}{15} = \frac{2}{3} \] So, the slope of the line is \( \frac{2}{3} \). To put this concept into perspective, slopes can transform straight lines into engaging graphics. Think of a slope of \( \frac{2}{3} \) as a hill where for every 2 units you move up, you move 3 units to the right. It's like walking up a gentle slope, perfect for a leisurely hike! Understanding slopes isn't just for math class; it has real-world applications! Engineers use slope calculations when designing roads, ensuring they are safe and comfortable to drive on. A gentle slope reduces the chances of cars skidding, while steeper slopes might require additional safety measures like guardrails. It's a mathematical principle that literally paves the way!