The graph you've uploaded shows a shaded region that is bounded by two straight lines, forming an inverted "V" shape with the vertex at the origin (0,0). The shaded region appears to be above these two lines, which means the inequality will represent this region.

Here’s how we can analyze the graph:

1. Identifying the boundary lines: The graph shows two boundary lines with negative and positive slopes, meeting at the origin (0,0).

   • The line on the left has a slope of -1, so its equation is $y = -x$.
   • The line on the right has a slope of 1, so its equation is $y = x$.

2. Shaded Region: The shaded region is above both lines, which suggests we are dealing with inequalities where $y$ is greater than or equal to both $-x$ and $x$. Since the boundary lines are included in the shading (solid lines), the inequality includes equality.

Thus, the inequalities that describe the shaded region are:

$y \leq |x|$

This inequality represents the region where $y$ is less than or equal to the absolute value of $x$, corresponding to the "V" shape with the vertex at the origin and shaded above.

Would you like further explanation or details?

Here are 5 related questions you might find useful:

1. How do absolute value inequalities work, and what do they represent?
2. How would the inequality change if the shaded region were below the lines?
3. What if the boundary lines were dashed instead of solid?
4. Can you write this inequality in terms of two separate inequalities without using absolute values?
5. How does the slope of the boundary lines affect the inequality?

Tip: When analyzing inequalities from graphs, always check whether the boundary lines are solid (inclusive) or dashed (exclusive).