Welcome! Today we will explore the linear function y equals x plus 6. This is a simple yet fundamental function in mathematics. Let's visualize it on a coordinate plane and understand its key characteristics.The y-intercept is where the line crosses the y-axis. To find it, we set x equals zero. When x is zero, y equals zero plus 6, which equals 6. Therefore, the y-intercept is at the point zero comma 6. This is a key feature of the function.The slope tells us how steep the line is. It is calculated as rise over run. For the function y equals x plus 6, the slope is 1. This means that for every 1 unit we move to the right, we move 1 unit up. Let's visualize this with a triangle showing the rise and run.The x-intercept is where the line crosses the x-axis. To find it, we set y equals zero. When y is zero, we have zero equals x plus 6. Solving for x, we get x equals negative 6. Therefore, the x-intercept is at the point negative 6 comma zero.Let's summarize the key properties of y equals x plus 6. The slope is 1, meaning the line rises at a 45-degree angle. The y-intercept is at zero comma 6, and the x-intercept is at negative 6 comma zero. This is a linear function with a positive slope, so it increases as x increases. Understanding these properties helps us analyze and graph linear functions effectively.