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

1. Identify the slope and y-intercept:

   • The equation is in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
   • Here, $m = 1$ (slope) and $b = 1$ (y-intercept).

2. Plot the y-intercept:

   • Start at the point $(0, 1)$ on the y-axis.

3. Use the slope to find another point:

   • The slope $m = 1$ means "rise over run" is $1/1$. From $(0, 1)$, move up 1 unit and right 1 unit to the point $(1, 2)$.
   • Alternatively, move down 1 unit and left 1 unit to $(-1, 0)$.

4. Draw the line:

   • Connect these points with a straight line extending in both directions.

Would you like me to plot this or provide additional steps for accuracy?

Related Questions:

1. What is the significance of the slope in a linear equation?
2. How do you convert other forms of linear equations (e.g., standard form) to slope-intercept form?
3. What happens if the slope is a fraction or a negative value?
4. How do parallel and perpendicular lines relate to the slopes of linear equations?
5. How would you graph a horizontal or vertical line?

Tip: When graphing, always check your points by substituting back into the original equation!