The translation of the equation y = x to y = x + 7 represents a vertical shift of the graph of the equation.
In this case, we are adding 7 to the y-value for every x-value. This means that for each point (x, y) on the original line y = x, the new point will be (x, y + 7). So if we take a point like (0, 0) from the graph of y = x, after the translation, it becomes (0, 7). Consequently, the entire graph moves up by 7 units.
Overall, this transformation does not change the slope or the direction of the line; it simply shifts the graph upwards, maintaining the original shape and orientation.