Let’s analyze the graph and the inequalities step by step.

1. Line A:

   • The slope of Line A is negative (downward slope). Using two points from the graph, the slope is $-1$ because it goes down $1$ unit for every $1$ unit to the right.
   • The $y$-intercept of Line A is $3$ (where the line crosses the $y$-axis).
   • The shaded region below Line A indicates the inequality is $y \leq -x + 3$.

2. Line B:

   • The slope of Line B is positive (upward slope). Using two points from the graph, the slope is $2$ because it rises $2$ units for every $1$ unit to the right.
   • The $y$-intercept of Line B is $-4$ (where the line crosses the $y$-axis).
   • The shaded region above Line B indicates the inequality is $y \geq 2x - 4$.

3. Shaded Region:

   • The shaded region is the overlapping solution area that satisfies both inequalities.

Final Inequalities:

• Line A: $y \leq -x + 3$
• Line B: $y \geq 2x - 4$

Would you like more explanation on the steps?

Related Questions:

1. How do you find the slope of a line from a graph?
2. What does the shaded region in a graph of inequalities represent?
3. How can you determine if an inequality includes equality ($\leq$ or $\geq$) or strict inequality ($<$ or $>$)?
4. How do you graph a system of linear inequalities?
5. What are some real-world applications of linear inequalities?

Tip:

Always test a point (e.g., $(0, 0)$) to verify which side of the line satisfies the inequality.