The inequality given is $x - y > -5$, which means the shaded region is the solution set for the inequality where $x - y > -5$. The boundary line $x - y = -5$ is dashed, indicating points on the line are not included in the solution.

To determine which points are solutions:

Step 1: Rewrite the inequality

$x - y > -5$ Rewriting it to isolate $y$: $y < x + 5$

This represents the region below the line $y = x + 5$ (not including the line itself).

Step 2: Test the given points

Substitute each point into $x - y > -5$ or equivalently $y < x + 5$:

1. (0, 0): $0 - 0 > -5$ is true (or $0 < 0 + 5$ is true). Solution.

2. (2, 5): $2 - 5 > -5$ is true (or $5 < 2 + 5$ is true). Solution.

3. (-1, 5): $-1 - 5 > -5$ is false (or $5 < -1 + 5$ is false). Not a solution.

4. (7, -12): $7 - (-12) > -5$ is true (or $-12 < 7 + 5$ is true). Solution.

5. (-4, 2): $-4 - 2 > -5$ is false (or $2 < -4 + 5$ is false). Not a solution.

Final Answer:

The points that satisfy the inequality are:

• (0, 0)
• (2, 5)
• (7, -12)

Would you like a detailed graph explanation?

Related Questions:

1. What is the difference between $>$ and $\geq$ in inequalities?
2. How can I graph a linear inequality step by step?
3. Why does a dashed line indicate points are not part of the solution?
4. How would the solution region change if the inequality were $x - y \leq -5$?
5. Can inequalities have multiple solution regions?

Tip: Always test points within the shaded region to ensure they satisfy the inequality.