The function provided is $f(x) = x + 6$, which is a linear equation of the form $y = mx + b$. Here:

• The slope $m = 1$, indicating that the line rises by 1 unit for every 1 unit it moves to the right.
• The y-intercept $b = 6$, meaning that the line crosses the y-axis at $y = 6$.

Steps to sketch the graph:

1. Identify the y-intercept: The graph will cross the y-axis at $(0, 6)$.
2. Use the slope: Since the slope is 1, you can plot another point by moving 1 unit right and 1 unit up from the y-intercept. This will give you the point $(1, 7)$.
3. Draw the line: After plotting the two points, draw a straight line through them. The line will have a positive slope and extend infinitely in both directions.

Would you like me to generate a graph for you based on this information?

Here are some questions you might want to explore further:

1. How does the slope of the line affect the steepness?
2. What would happen to the graph if the slope were negative?
3. How do you find the x-intercept of this line?
4. Can you express this equation in another form, like point-slope form?
5. What would happen to the graph if the y-intercept were negative?

Tip: When sketching linear functions, always start with the y-intercept, and use the slope to guide the direction of the line.