To solve the equation \( y = -x + 1 \), we can rewrite it in a standard form. This equation represents a line with a slope of -1 and a y-intercept of 1.

### Steps to understand this equation:

1. **Identify the Slope and Y-Intercept**:
   - The slope (m) is -1.
   - The y-intercept (b) is 1, meaning the line crosses the y-axis at (0, 1).

2. **Find the X-Intercept**:
   - Set \( y = 0 \):
   \[
   0 = -x + 1 \implies x = 1
   \]
   So, the x-intercept is (1, 0).

3. **Graphing the Equation**:
   - Plot the points (0, 1) and (1, 0).
   - Draw a line through these points.

### Summary
The equation \( y = -x + 1 \) describes a linear relationship where y decreases as x increases, intersecting the y-axis at 1 and the x-axis at 1.

Would you like further details on graphing or solving equations? Here are some related questions:

1. What does the graph of \( y = -x + 1 \) look like?
2. How would you find the slope and intercept of another linear equation?
3. Can you provide examples of equations with different slopes?
4. What are the applications of linear equations in real life?
5. How can you solve systems of equations involving this line?

**Tip**: Always check if an equation is in slope-intercept form (y = mx + b) to quickly identify its slope and intercepts.

Explore the linear equation y = -x + 1, including its slope, intercepts, and how to graph it. This page provides a step-by-step explanation of the equation's characteristics and its applications. Ideal for Grades 7-9 students.

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