Find the slope of the line passing through the points \( (-4,-4) \) and \( (2,5) \).

To find the slope of the line passing through the points \( (-4,-4) \) and \( (2,5) \), we can use the formula for slope \( m \) given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, let \( (x_1, y_1) = (-4, -4) \) and \( (x_2, y_2) = (2, 5) \). Plugging in the values: \[ m = \frac{5 - (-4)}{2 - (-4)} = \frac{5 + 4}{2 + 4} = \frac{9}{6} = \frac{3}{2} \] So, the slope of the line is \( \frac{3}{2} \). For anyone who loves numbers, understanding slopes might feel like learning a secret code! It tells you how steep a line is and the direction it takes. Positive slopes mean the line rises as it moves to the right, and negative slopes indicate it falls. The fun part? You can visualize this concept with a hill; if you climb up, it’s a positive slope, but if you’re sliding down, it’s negative! In real life, this slope concept appears everywhere! Think of it like the road you're driving on. A steep hill has a higher slope, so if you’re hiking up that mountain, you'll need to work a bit harder, just like your car will struggle more going uphill than on a flat road! The slope helps you understand the steepness and can guide you in planning the best path for your journey.