The graph you provided displays a linear inequality, and we are tasked with writing the inequality in slope-intercept form, which is generally expressed as:

$y \leq mx + b$ or $y \geq mx + b$ depending on the shading of the graph.

Steps to Determine the Inequality:

1. Identify the boundary line: The boundary line appears solid, meaning the inequality will include "≤" or "≥" (the solution set includes the boundary line).

2. Find the slope: The line passes through two distinct points:

   • (0, 8)
   • (8, 0)

   We can use these points to find the slope $m$ using the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 8}{8 - 0} = \frac{-8}{8} = -1$

   Thus, the slope $m = -1$.

3. Find the y-intercept: The y-intercept $b$ is the point where the line crosses the y-axis. From the graph, this happens at $(0, 8)$, so $b = 8$.

4. Write the equation of the boundary line: Using the slope-intercept form of a line $y = mx + b$: $y = -x + 8$

5. Determine the inequality symbol: The shading is below the boundary line, meaning the inequality is $\leq$. Thus, the inequality that represents the graph is:

   $y \leq -x + 8$

Final Inequality:

$y \leq -x + 8$

Would you like further clarification or details?

Here are five related questions to expand your understanding:

1. How do we interpret the shading in a linear inequality graph?
2. What happens if the boundary line is dashed instead of solid?
3. How do we handle cases where the slope is a fraction?
4. What is the significance of the y-intercept in a linear inequality?
5. Can you graph the inequality $y \geq 2x - 3$?

Tip: When determining the slope from a graph, choose two points with integer coordinates to avoid calculation errors.