To graph the line for the equation $y = x + 1$, follow these steps:

1. Understand the equation format: The equation $y = x + 1$ is in slope-intercept form, which is $y = mx + b$. Here:

   • The slope $m$ is 1.
   • The y-intercept $b$ is 1 (this is the point where the line crosses the y-axis).

2. Plot the y-intercept: Start by plotting the point $(0, 1)$ on the graph, because when $x = 0$, $y = 1$.

3. Use the slope: The slope is $m = 1$, which means "rise over run" is $1/1$. From the y-intercept, move up 1 unit and 1 unit to the right to plot the next point. This gives you the point $(1, 2)$.

4. Plot additional points: Continuing with the slope, plot more points like $(2, 3)$, $(3, 4)$, and so on.

5. Draw the line: Once you have enough points, draw a straight line through them. This will be the graph of the equation $y = x + 1$.

Would you like more details or help with any other questions?

Here are five related questions to deepen your understanding:

1. How would you graph a line with a negative slope, such as $y = -x + 1$?
2. What happens to the graph if you change the y-intercept (e.g., $y = x - 2$)?
3. How do you graph a vertical line, such as $x = 3$?
4. What is the difference between graphing $y = x + 1$ and graphing $2y = 2x + 2$?
5. How do you find the slope of a line if you're only given two points?

Tip: Always identify the slope and intercept first when graphing from the slope-intercept form equation.