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To graph the inequality \(-3x - 2y > 2\), let's follow these steps:

### Step 1: Rewrite the inequality in slope-intercept form
The standard form for slope-intercept is \(y = mx + b\). We need to solve for \(y\):

\[
-3x - 2y > 2
\]

\[
-2y > 3x + 2
\]

\[
y < -\frac{3}{2}x - 1
\]

### Step 2: Graph the boundary line
The boundary line for the inequality \(y = -\frac{3}{2}x - 1\) is plotted as a dashed line because the inequality is strict (does not include the line itself, \(>\) or \(<\)).

- The y-intercept is at \((0, -1)\).
- The slope is \(-\frac{3}{2}\), meaning that for every 2 units you move to the right, you move 3 units down.

Plot these points on the graph:
1. Start at the point \((0, -1)\).
2. Move 2 units to the right and 3 units down to get another point, \((2, -4)\).

Draw a dashed line through these points.

### Step 3: Shade the correct region
Since the inequality is \(y < -\frac{3}{2}x - 1\), you will shade the region below the dashed line.

This shaded area represents all the points \((x, y)\) that satisfy the inequality.

Would you like a more detailed explanation or have any questions?

### Related Questions
1. How do you graph inequalities with a slope that is a fraction?
2. What changes when the inequality is \( \geq \) or \( \leq \)?
3. How do you determine which side of the line to shade?
4. What does it mean when an inequality is not strict (has \( \geq \) or \( \leq \))?
5. Can we use test points to check which region to shade for the inequality?

### Tip
Always remember to use a dashed line for strict inequalities (\(<\) or \(>\)) and a solid line for non-strict inequalities (\(\leq\) or \(\geq\)).

Learn how to graph the linear inequality -3x - 2y > 2 using slope-intercept form. This tutorial covers converting the inequality into slope-intercept form, graphing the boundary line, and shading the correct region. Suitable for students in Grades 8-10.

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