A straight line that passes through \( (-1,4) \) and \( (3,-4) \). The equation of the line is

To find the equation of the line that passes through the points \((-1, 4)\) and \((3, -4)\), we first calculate the slope, \(m\), using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 - 4}{3 - (-1)} = \frac{-8}{4} = -2. \] Next, we can use the point-slope form of the line's equation, \(y - y_1 = m(x - x_1)\). Using point \((-1, 4)\): \[ y - 4 = -2(x + 1). \] Distributing gives: \[ y - 4 = -2x - 2, \] \[ y = -2x + 2. \] Therefore, the equation of the line is \(y = -2x + 2\). Now, onto some fun facts! The concept of slope is crucial not just in math but also in everyday life! It’s essentially about how steep something is, like the angle of a ramp or the incline of a hill. A negative slope indicates a downhill direction—so think of it as the path of a thrilling roller coaster descent! Ever heard of two-dimensional graphs being used in real-world applications? They are! Graphs help in plotting data points, like tracking sales over time or the relationship between height and weight. So next time you're making a chart or analyzing trends, remember, you’re using those same principles!