The image presents a problem involving a linear inequality and a question about determining whether a point lies within a shaded region.

The inequality shown is: $y \geq -2x + 3$ The problem asks if the point $(-2, 4)$ satisfies this inequality.

Steps to Solve:

1. Substitute the coordinates of the point $(-2, 4)$ into the inequality to check if it's a solution:

   • The inequality is $y \geq -2x + 3$.
   • For the point $(-2, 4)$, $x = -2$ and $y = 4$.

2. Substitute into the equation: $4 \geq -2(-2) + 3$ Simplifying the right-hand side: $4 \geq 4 + 3$ $4 \geq 7$

3. Conclusion: The inequality $4 \geq 7$ is false. Therefore, the point $(-2, 4)$ does not satisfy the inequality.

In the sketch provided, it appears there's a graph of the inequality, with shading showing the region that satisfies the inequality. The point $(-2, 4)$ falls outside the shaded region, confirming that it is not a solution.

Would you like further details on solving inequalities or graphing them? Here are a few follow-up questions for practice:

1. How do you graph a linear inequality like $y \geq -2x + 3$?
2. What changes when the inequality symbol is $>$ instead of $\geq$?
3. What does the boundary line represent in the context of an inequality?
4. How do you determine the shaded region in an inequality graph?
5. Can a point lie exactly on the boundary line and still satisfy the inequality?

Tip: When graphing linear inequalities, the boundary line is solid for $\geq$ or $\leq$ and dashed for $>$ or $<$.