We begin by introducing the linear function y equals x plus 67. This is a simple linear equation where the slope is 1 and the y-intercept is 67. Let's visualize this function on a coordinate plane.The slope of our line is 1. This tells us the rate of change. For every 1 unit we move right along the x-axis, the y-value increases by exactly 1 unit. We can see this by examining two points on the line and calculating the rise over run.The y-intercept of our function is 67. This is the point where the line crosses the y-axis. When x equals 0, y equals 67. This constant term shifts the entire line upward by 67 units compared to the basic line y equals x.Now let's evaluate the function at several specific x-values. When x is negative 5, y equals 62. When x is 0, y is 67. When x is 5, y becomes 72. And when x is 10, y equals 77. Notice how each increase of 5 in x results in an increase of 5 in y, confirming our slope of 1.In summary, y equals x plus 67 is a linear function with a slope of 1 and a y-intercept of 67. This type of function has many real-world applications, such as converting between temperature scales, calculating costs with fixed fees, or modeling any linear relationship where there is a constant rate of change plus a fixed starting value.