The translation of the graph of the equation y = x to the equation y = x + 7 involves a vertical shift. In this case, the entire graph of the line represented by y = x is moved upwards by 7 units on the y-axis.
To understand this transformation better, consider the following:
1. **Original Equation:** The original line y = x has a slope of 1, which means for every unit increase in x, y also increases by 1. This line passes through the origin (0, 0).
2. **New Equation:** The new line y = x + 7 retains the same slope of 1, but the addition of 7 indicates that every point on the original line is now 7 units higher. For example, the point (0, 0) on the original line translates to the point (0, 7) on the new line.
3. **Graphical Representation:** If you were to plot these two lines on a graph, you’d see that they are parallel to each other since they have the same slope, but the second line is consistently higher by 7 units. This upward translation maintains the steepness of the line while altering its intercept with the y-axis.
In summary, the translation from y = x to y = x + 7 can be described as a vertical translation of 7 units upward on the graph.