The equation you're asked to graph is $y = x + 6$. This is the equation of a straight line in slope-intercept form, $y = mx + b$, where:

• $m = 1$ is the slope of the line.
• $b = 6$ is the y-intercept, which means the line crosses the y-axis at the point (0, 6).

Steps to graph the equation:

1. Plot the y-intercept:

   • Start by marking the point (0, 6) on the y-axis, since $b = 6$.

2. Use the slope to find another point:

   • The slope $m = 1$ tells you to move 1 unit up and 1 unit to the right for each point. From (0, 6), go to (1, 7), then (2, 8), and so on.
   • Alternatively, you can go in the negative direction: move 1 unit down and 1 unit left, reaching (-1, 5), (-2, 4), etc.

3. Draw the line:

   • Connect all these points with a straight line.

Verifying the graph:

• From the image, I can see a grid that is ready to be used for plotting. Start by marking the point (0, 6) on the y-axis, then follow the slope to place more points as described.

Would you like to discuss this further or need help with another problem?

Follow-up questions:

1. What does the slope of 1 mean in this equation?
2. How would you graph $y = 2x + 6$?
3. If the equation was $y = x - 3$, how would the graph change?
4. How does changing the slope affect the steepness of the line?
5. Can you identify the x-intercept of this line?

Tip: Always start with the y-intercept and use the slope to determine how the line inclines or declines.