Find the slope of the line passing through the points \( (-2,9) \) and \( (-5,5) \)

To find the slope of the line passing through the points \( (-2,9) \) and \( (-5,5) \), you use the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \( (x_1, y_1) = (-2, 9) \) and \( (x_2, y_2) = (-5, 5) \). Plugging in these values: \[ m = \frac{5 - 9}{-5 + 2} = \frac{-4}{-3} = \frac{4}{3} \] So, the slope of the line is \( \frac{4}{3} \). Finding slopes like this one is super important in various fields! For instance, in architecture and engineering, understanding how steep a ramp, roof, or road needs to be directly ties back to calculating slopes. A small slope can mean a gentle ramp that's easier for people with mobility issues, while a steeper slope may be preferred for quick drainage on a road. When calculating slopes, one common mistake is mixing up the coordinates. Always ensure \( (x_1, y_1) \) and \( (x_2, y_2) \) are correctly assigned. Also, be careful with subtracting negatives—double-check your signs! A small oversight here can completely alter your slope calculation.