Let's analyze the image and determine the inequality representing the shaded region.

Steps:

1. Identify the line equation: The black line shown forms the boundary of the shaded region. We need to find its equation.
2. Slope-Intercept Form: This line equation appears to be in the form $y = mx + c$, where $m$ is the slope and $c$ is the y-intercept.
3. Determine the inequality: Based on the shading, we will identify whether the inequality is $\leq, \geq, <,$ or $>$.

Observations:

• The line passes through:
  • Point $(0, 3)$ (y-intercept).
  • Point $(6, 0)$.
• Slope $m$ can be calculated: $m = \frac{\text{change in } y}{\text{change in } x} = \frac{3 - 0}{0 - 6} = -\frac{1}{2}.$
• Hence, the equation of the line is: $y = -\frac{1}{2}x + 3.$

Shading:

The shaded region lies below the line, meaning the inequality is: $y \leq -\frac{1}{2}x + 3.$

Would you like a step-by-step explanation of the calculations or more details? Let me know!

Related Questions:

1. How do you calculate the slope of a line between two points?
2. How do you determine whether to use $\leq, \geq, <,$ or $>$ in inequalities?
3. What does the y-intercept of a line represent?
4. How can you check if a point satisfies an inequality?
5. How do graphing tools help visualize inequalities?

Tip:

Always test a point in the shaded region (e.g., $(0, 0)$) to confirm the inequality's direction!