To write an inequality represented by the graph with the boundary line $5x + 2y = 6$, we need to determine which side of the line the shaded region represents.

Given the boundary line: $5x + 2y = 6$ we can follow these steps to establish the inequality:

1. Rewrite the equation in slope-intercept form to help visualize the inequality: $2y = -5x + 6 \Rightarrow y = -\frac{5}{2}x + 3$

2. Determine which side of the line is shaded: If the region above the line is shaded, the inequality would be $y > -\frac{5}{2}x + 3$. If the region below the line is shaded, it would be $y < -\frac{5}{2}x + 3$.

3. Choose the correct inequality sign based on the shaded region: Since I don’t have direct shading information here, check where the shading lies relative to the boundary line.

4. Final Inequality:

   • If the shaded area is above the line, the inequality is $5x + 2y < 6$.
   • If the shaded area is below the line, the inequality is $5x + 2y > 6$.

Verify the shading to confirm the inequality sign.

Would you like further details on graphing or solving inequalities?

Here are related questions that expand on this concept:

1. How do we determine the inequality direction when the graph is shaded?
2. What methods can we use to convert standard form to slope-intercept form?
3. How would the inequality change if the boundary line were dashed instead of solid?
4. How do we test if a point satisfies a given inequality?
5. How can we interpret inequalities in real-world applications?

Tip: When unsure about shading, test a point (like the origin) to see if it satisfies the inequality.