What is the slope of the line that passes through the points \( (-2,-4) \) and \( (5,1) \) ? \( 7 / 5 \) \( -7 / 5 \) \( 5 / 7 \) \( -5 / 7 \)

To find the slope of the line that passes through the points \((-2,-4)\) and \((5,1)\), you use the formula for slope \(m\): \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Plugging in the coordinates: \[ m = \frac{1 - (-4)}{5 - (-2)} = \frac{1 + 4}{5 + 2} = \frac{5}{7} \] So, the slope of the line is \(\frac{5}{7}\). Both historical mathematicians and modern-day scientists frequently rely on the fundamental concept of slope. The slope not only illustrates the steepness of a line but is also crucial for understanding real-world scenarios like the rate of change in economics, physics, and even simple activities like climbing a hill! If you’re new to calculating slopes, a common mistake is confusing the order of points. Always ensure you stick to the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\) and remember that the coordinates must be in the correct order to avoid negative slopes or incorrect values.