Determine the slope of the line through the given points. \[ (5,-10) \text { and }(3,-1) \]

To find the slope of the line that passes through the points \( (5, -10) \) and \( (3, -1) \), you can use the formula for slope, which is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Assigning the points, let \( (x_1, y_1) = (5, -10) \) and \( (x_2, y_2) = (3, -1) \). Now plug in the values: \[ m = \frac{-1 - (-10)}{3 - 5} = \frac{-1 + 10}{3 - 5} = \frac{9}{-2} = -\frac{9}{2} \] So, the slope of the line through the points \( (5, -10) \) and \( (3, -1) \) is \( -\frac{9}{2} \). Now here are some fun facts: Understanding the slope is crucial because it not only tells you the steepness of a line but also the direction. A positive slope means the line is rising, while a negative slope (like ours!) indicates it's falling. Think of it as a rollercoaster that dives down when you move from left to right! In practical terms, slopes are everywhere—from determining the incline of a roof to figuring out speed on a bike. If you’re building something like a ramp, knowing how to calculate a slope ensures it's safe and functional. Plus, if anyone asks why you can navigate slopes like a pro, you can impress them with your math skills!