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The equation given is \( y = -x + 3 \), which is a linear equation in slope-intercept form, \( y = mx + b \), where:
- \( m = -1 \) (the slope)
- \( b = 3 \) (the y-intercept).

### To plot this:
1. **Y-intercept**: The line crosses the y-axis at \( (0, 3) \).
2. **Slope**: The slope of -1 means for every 1 unit increase in \( x \), \( y \) decreases by 1. This gives a downward-sloping line from left to right.

### Key points to plot:
- Start with the point \( (0, 3) \).
- From \( (0, 3) \), move 1 unit to the right to \( x = 1 \) and 1 unit down, arriving at \( (1, 2) \).
- You can continue this process, moving points down and to the right, or alternatively move up and to the left to plot more points like \( (-1, 4) \).

### Graph description:
The line will pass through points such as:
- \( (0, 3) \)
- \( (1, 2) \)
- \( (2, 1) \)
- \( (-1, 4) \)
It slopes downwards with a slope of -1, representing a consistent decline as \( x \) increases.

Would you like a detailed step-by-step solution for how to plot linear equations like this? Also, here are some related questions to expand your understanding:

1. What does the slope of a line represent in general?
2. How does changing the y-intercept affect the position of a line on a graph?
3. What happens if the slope is positive instead of negative?
4. How would the graph change if the equation were \( y = -2x + 3 \)?
5. Can you derive the slope-intercept form from a standard form equation, \( Ax + By = C \)?

**Tip:** For linear equations, always identify the slope and intercept to quickly understand how the line behaves and where it crosses the axes.

Learn how to graph the linear equation y = -x + 3. This guide covers key algebraic concepts like slope, y-intercept, and graphing techniques. Suitable for students in Grades 7-10.

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