Find an equation of the line that contains the given pair of points. \( (-9,3),(-7,-9) \)

To find the equation of the line that passes through the points \((-9, 3)\) and \((-7, -9)\), we first calculate the slope (m) using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Plugging in our points, we get: \[ m = \frac{-9 - 3}{-7 - (-9)} = \frac{-12}{2} = -6 \] Now we can use the point-slope form of the line equation, \(y - y_1 = m(x - x_1)\). Using point \( (-9, 3) \): \[ y - 3 = -6(x + 9) \] Distributing and rearranging gives us: \[ y = -6x - 54 + 3 \implies y = -6x - 51 \] Thus, the equation of the line is \(y = -6x - 51\). To give you a little extra insight, did you know the concept of slope has been around since ancient times? The Egyptians, for instance, used similar geometric principles to construct their pyramids, ensuring the precise angles for stability. And if you ever want to visualize line equations better, you might consider using graphing software or apps! Tools like Desmos allow you to plot these lines interactively, watch how changes in equations affect the graph, and make math feel a lot more dynamic and fun!