ind an equation of the line containing the given pair of points. \[ (-4,-4) \text { and }(4,4) \] The equation of the line is \( y=\square \). (Simplify your answer. Type your answer in slope-intercept form. Use integers or fractic

To find the equation of the line through the points \((-4,-4)\) and \((4,4)\), we start by calculating the slope \(m\) using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Plugging in our points: \[ m = \frac{4 - (-4)}{4 - (-4)} = \frac{8}{8} = 1. \] Now that we have the slope, we can use the point-slope form of the equation: \(y - y_1 = m(x - x_1)\). Using the point \((-4, -4)\): \[ y - (-4) = 1(x - (-4)) \Rightarrow y + 4 = x + 4. \] Simplifying this yields: \[ y = x. \] So the equation of the line is \(y = 1x + 0\) or simply \(y = x\). Did you know that the line \(y = x\) is a perfect example of a function? It’s not just any function though—it represents a direct correlation where every x-value results in the same y-value, making it a useful reference point in various fields, especially in physics and engineering! If you're ever unsure of your calculations, keep in mind that graphing your points can be a lifesaver! Plotting the points on a coordinate plane helps ensure you've got your slope and intercepts right. A common mistake is forgetting to simplify the $(x,y)$ relationship in slope-intercept form, but with a little practice, you'll nail it every time!