The graph shows a linear inequality. From the image, we can break the problem down as follows:

1. Identify the boundary line: The line appears to pass through two points:

   • $(-5, 3)$
   • $(2, 1)$

   To find the equation of the line, we calculate the slope (m):

   $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 3}{2 - (-5)} = \frac{-2}{7}$

   So, the slope $m = -\frac{2}{7}$.

   Using the point-slope form of the line $y - y_1 = m(x - x_1)$, let's use the point $(2, 1)$:

   $y - 1 = -\frac{2}{7}(x - 2)$

   Simplifying:

   $y - 1 = -\frac{2}{7}x + \frac{4}{7}$

   $y = -\frac{2}{7}x + \frac{4}{7} + 1$

   $y = -\frac{2}{7}x + \frac{11}{7}$

2. Determine the inequality: The shaded region is below the line, which suggests that the inequality is $\leq$ or $<$. Since the boundary line is solid, the inequality is $\leq$.

Thus, the inequality represented by the graph is:

$y \leq -\frac{2}{7}x + \frac{11}{7}$

Would you like further details or have any questions?

5 Related Questions:

1. How do you graph an inequality with a non-solid boundary line?
2. Can an inequality have more than one shaded region?
3. What happens when an inequality flips its sign (e.g., from $\leq$ to $\geq$) in a graph?
4. How does changing the slope affect the graph of a linear inequality?
5. What is the significance of testing points to determine the correct shaded region?

Tip:

Always test a point (like $(0, 0)$, if not on the line) to verify which side of the line should be shaded when graphing inequalities.