To solve this problem, we need to determine the inequality that represents the shaded region on the graph.

Step 1: Find the equation of the boundary line.

The boundary line is given as a dashed line, which indicates that the inequality will be either "<" or ">".

• To find the equation of the line, observe the slope and y-intercept.
• The line crosses the y-axis at $y = 8$ and the x-axis at $x = -8$.

The slope $m$ of the line can be calculated as:

$m = \frac{\text{change in } y}{\text{change in } x} = \frac{8 - 0}{0 - (-8)} = \frac{8}{8} = 1$

Thus, the equation of the line is:

$y = -x + 8$

Step 2: Determine the inequality.

The shading is below the line, which means we are looking for the region where $y$ is less than the line:

$y < -x + 8$

However, since the line is dashed, the inequality should be strict (i.e., "<" rather than "≤").

Final Answer:

The inequality that represents the shaded region is:

$y < -x + 8$

Would you like further details or have any questions?

Follow-up Questions:

1. What if the line had been solid instead of dashed?
2. How would the inequality change if the shading was above the line?
3. What is the slope-intercept form of a line?
4. How do you determine the slope from a graph?
5. Can you express the inequality in standard form?
6. What does the inequality $y > -x + 8$ represent?
7. How would you graph the inequality $y \geq -x + 8$?
8. How can you verify if a point satisfies the inequality?

Tip:

When identifying an inequality from a graph, always check if the boundary line is dashed (indicating strict inequality) or solid (indicating inclusive inequality).