https://file.aiquickdraw.com/mathbot/file/1727209653402dgc0mutw.jpg

To describe the unshaded region in the graph with two inequalities, let's analyze the lines in the diagram:

1. **Black Solid Line (Diagonal Line)**:
   This line passes through the points \((0, 3)\) and \((6, 0)\). The slope \(m\) of the line can be calculated using the formula:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 3}{6 - 0} = -\frac{1}{2}
   \]
   The equation of this line in slope-intercept form \(y = mx + b\) becomes:
   \[
   y = -\frac{1}{2}x + 3
   \]
   Since the unshaded region is below this solid line, the inequality for this line is:
   \[
   y \leq -\frac{1}{2}x + 3
   \]

2. **Dashed Line**:
   This line passes through the points \((0, 6)\) and \((6, 0)\). The slope is:
   \[
   m = \frac{0 - 6}{6 - 0} = -1
   \]
   The equation of this line is:
   \[
   y = -x + 6
   \]
   Since the unshaded region is below this dashed line, and it's a dashed line (which indicates strict inequality), the inequality for this line is:
   \[
   y < -x + 6
   \]

### Final Inequalities:
- \( y \leq -\frac{1}{2}x + 3 \)
- \( y < -x + 6 \)

These inequalities describe the unshaded region.

Would you like more details or have any questions?

### Follow-up questions:
1. How would the inequalities change if the shaded region were considered instead of the unshaded one?
2. What do the dashed and solid lines represent in terms of inequality symbols?
3. How do you calculate the slope of a line given two points?
4. Can you identify the y-intercepts of these two lines from the graph?
5. How would the inequalities change if the graph had vertical or horizontal lines?

**Tip:** Always check whether a line is solid or dashed in graph problems involving inequalities. This tells you whether the inequality is inclusive or strict.

Write down the two inequalities that describe the unshaded region in the diagram below.

This problem involves determining the inequalities that describe the unshaded region of a graph. It covers key concepts such as the slope formula, graphing linear equations, and interpreting solid and dashed lines in inequalities. Suitable for students in Grades 8-10.

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