To graph the equation \( y = -2x + 3 \), follow these steps:

1. **Identify the slope and y-intercept**:  
   - The slope (\( m \)) is \(-2\), which means for every 1 unit increase in \( x \), \( y \) decreases by 2 units.
   - The y-intercept (\( b \)) is \( 3 \), which means the line crosses the y-axis at the point \( (0, 3) \).

2. **Plot the y-intercept**:  
   - Start by plotting the point \( (0, 3) \) on the graph.

3. **Use the slope to find another point**:  
   - From the y-intercept \( (0, 3) \), move 1 unit to the right (increase \( x \) by 1) and 2 units down (since the slope is \(-2\)), landing at the point \( (1, 1) \).
   - Plot this point \( (1, 1) \) on the graph.

4. **Draw the line**:  
   - Draw a straight line through the points \( (0, 3) \) and \( (1, 1) \). This line is the graph of the equation \( y = -2x + 3 \).

Would you like a detailed image of the graph? 

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Here are 5 relative questions to consider:

1. How would the graph change if the slope was positive?
2. What happens to the graph if the y-intercept changes to -3?
3. How would you graph \( y = 2x + 3 \), and how does it differ from \( y = -2x + 3 \)?
4. How can you determine the x-intercept of the line \( y = -2x + 3 \)?
5. How would the graph look if the equation were \( y = -2x \) (no y-intercept)?

**Tip:** When graphing, always start with the y-intercept and use the slope to find other points on the line for accuracy.

Learn how to graph the linear equation y = -2x + 3 with detailed step-by-step instructions. Understand the concepts of slope and y-intercept in graphing linear equations. Suitable for students in Grades 7-9.

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