To graph the inequality $y \leq x - 2$ as a system of linear inequalities, we first need to understand that this inequality involves a boundary line and a shaded region.

Step 1: Graph the Boundary Line

The inequality $y \leq x - 2$ includes the line $y = x - 2$, which is a linear equation with a slope of 1 and a y-intercept at -2. This line will be solid (not dashed) because the inequality is "less than or equal to," meaning points on the line satisfy the inequality.

1. Start by plotting the y-intercept at (0, -2).
2. Use the slope (1) to find another point by moving up 1 unit and right 1 unit.
3. Draw a solid line through these points.

Step 2: Determine the Shaded Region

Since the inequality is $y \leq x - 2$, we shade the region below the line, as that represents all points where $y$ is less than or equal to $x - 2$.

Representing as a System of Inequalities

If you're instructed to show this as a "system," we could interpret that as potentially adding a restriction on the domain or range. Without additional constraints, however, the inequality $y \leq x - 2$ alone defines the region.

Would you like me to delve deeper into creating a system with multiple inequalities, or do you have any specific questions about graphing this?

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Related Questions:

1. How do you graph $y > x - 2$ instead?
2. What changes if the inequality is strict ($y < x - 2$)?
3. How would you graph $y \geq x - 2$ instead?
4. What is the role of the slope and y-intercept in this inequality?
5. How does shading differ for a vertical or horizontal line inequality?

Tip: Always start with the boundary line, then decide shading based on the inequality sign.