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To graph the equation \( y = -\frac{3}{2}x - 3 \), we’ll analyze the line in terms of its slope and y-intercept. Here’s a step-by-step approach:

### Step 1: Identify Slope and y-Intercept
The equation is in slope-intercept form, \( y = mx + b \), where:
- \( m = -\frac{3}{2} \) (slope)
- \( b = -3 \) (y-intercept)

### Step 2: Plot the y-Intercept
The y-intercept, \( b = -3 \), means the line crosses the y-axis at \( (0, -3) \). Plot this point on the graph.

### Step 3: Use the Slope to Find Another Point
The slope \( -\frac{3}{2} \) indicates that for every 2 units moved to the right (positive x-direction), the line goes down by 3 units (negative y-direction).

Starting from \( (0, -3) \):
- Move 2 units to the right (x increases by 2).
- Move down 3 units (y decreases by 3), reaching the point \( (2, -6) \).

Plot \( (2, -6) \) on the graph.

### Step 4: Draw the Line
Draw a straight line through these two points, \( (0, -3) \) and \( (2, -6) \), extending it in both directions.

### Verifying the Provided Graph
The uploaded image does not match this expected line for \( y = -\frac{3}{2}x - 3 \). The graph in the image is a horizontal line, which does not align with the negative slope given in the equation.

Would you like further details or have any questions?

### Related Questions:
1. How would you graph an equation with a positive slope?
2. What is the general form of a line equation, and how can it be transformed into slope-intercept form?
3. How can we verify if a point lies on a line given by an equation?
4. What would the graph look like if the slope was changed to \( \frac{3}{2} \)?
5. How do you find the x-intercept of a line given in slope-intercept form?

### Tip:
When graphing lines, always start by plotting the y-intercept and use the slope to find additional points.

Learn how to graph the equation y = -3/2 x - 3 using slope-intercept form. This guide explains key concepts like identifying slope and y-intercept and using them to plot points on a graph. Perfect for students in Grades 8-10.

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