The equation given is $y = x - 2$. This is in slope-intercept form, $y = mx + b$, where $m$ is the slope, and $b$ is the y-intercept.

Key Steps to Identify the Correct Graph:

1. Y-Intercept ($b$):

   • The y-intercept is $-2$. This means the graph crosses the y-axis at $(0, -2)$.

2. Slope ($m$):

   • The slope is $1$, which means the line rises 1 unit for every 1 unit it moves to the right.

3. Choose the Correct Graph:

   • Check which graph starts at $(0, -2)$ and has a slope of $1$. This means a diagonal line that goes upward to the right.

Based on the two options provided:

• The left graph shows a slope of 1 and intercepts the y-axis at $-2$. Therefore, the left graph is the correct representation of $y = x - 2$.

Would you like more details or have further questions about this? Here are some related questions:

1. What is the general approach to identifying graphs of linear equations?
2. How can the slope-intercept form help in sketching graphs manually?
3. What are the common mistakes when interpreting the slope and y-intercept?
4. How can we verify if a point lies on the line of a given equation?
5. How would the graph change if the slope or intercept is modified?

Tip: Always check the y-intercept first and then verify the slope when matching graphs to equations.