Which equation represents a line that passes through the point \( (-3,6) \) and \( (1,-6) \) ? A \( \quad y=-4 x-6 \) B \( y=-3 x-3 \) C \( y=-3 x \) D \( y=-2 x-4 \)

To find the equation of the line that passes through the points \((-3, 6)\) and \( (1, -6)\), we first need to calculate the slope \(m\): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-6 - 6}{1 - (-3)} = \frac{-12}{4} = -3 \] Now, we will use the point-slope form of the equation of a line, \(y - y_1 = m(x - x_1)\). Using the point \((-3, 6)\): \[ y - 6 = -3(x + 3) \] Expanding this: \[ y - 6 = -3x - 9 \] \[ y = -3x - 3 \] Thus, the equation that represents the line is \(y = -3x - 3\), so the correct answer is **B**. For a bit of history, did you know that the concept of the slope-intercept form was popularized by mathematician George Stokes in the 19th century? It allowed people to easily understand how lines behave, enabling complex geometric interpretations and serving as a foundational tool in algebra! In practical scenarios, you might encounter the need to find an equation of a line in various fields like engineering or economics. When dealing with real-world data, knowing how to derive the line that best fits the points can help model trends effectively, which is fundamental for project planning or sales forecasting.