https://file.aiquickdraw.com/mathbot/file/1729696899314u9htjdw6.jpg

The graph shows a linear inequality with the shaded region above the line and the boundary being a solid line, indicating that the boundary is part of the solution (i.e., it includes "equal to" in the inequality).

1. The slope of the line is \(-\frac{1}{3}\), which you can determine by calculating the change in \(y\) over the change in \(x\) between two points on the line, for example \((0, 2)\) and \((-6, 4)\). The slope formula is:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 2}{-6 - 0} = \frac{2}{-6} = -\frac{1}{3}
   \]

2. The y-intercept is \(2\) because the line crosses the y-axis at the point \((0, 2)\).

Thus, the equation of the line is \(y = -\frac{1}{3}x + 2\).

3. Since the region above the line is shaded, we know that \(y\) is greater than or equal to the expression \(-\frac{1}{3}x + 2\).

Therefore, the correct inequality represented by the graph is:
\[
y \geq -\frac{1}{3}x + 2
\]
So the correct answer is **D**.

Would you like further details on any part of this explanation?

Here are 5 related questions you might find interesting:
1. How do you determine the slope of a line from a graph?
2. What is the difference between a dashed line and a solid line in an inequality graph?
3. How do you graph linear inequalities?
4. Can inequalities have curved boundaries, and how would that be represented on a graph?
5. How do you solve a system of inequalities graphically?

**Tip**: When interpreting a shaded region, always check if the boundary line is solid or dashed to determine whether the inequality includes "equal to".

Understand how to determine a linear inequality from a graph where the slope is -1/3, the y-intercept is 2, and the shaded region is above the line. Learn the steps for calculating the slope and interpreting the solid line for inequality inclusion. Suitable for students in Grades 7-10.

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