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The given equation is \( y = -x + 4 \), which is a linear equation in slope-intercept form (\(y = mx + b\)), where:
- \(m = -1\) is the slope.
- \(b = 4\) is the y-intercept.

### Finding the Intercepts:

1. **Y-intercept**:
   The y-intercept occurs when \(x = 0\). Substituting \(x = 0\) into the equation:
   \[
   y = -(0) + 4 = 4
   \]
   So, the y-intercept is \( (0, 4) \).

2. **X-intercept**:
   The x-intercept occurs when \(y = 0\). Setting \(y = 0\) in the equation:
   \[
   0 = -x + 4
   \]
   Solving for \(x\):
   \[
   x = 4
   \]
   So, the x-intercept is \( (4, 0) \).

### Summary:
- **X-intercept**: \( (4, 0) \)
- **Y-intercept**: \( (0, 4) \)

Now you can graph the line by plotting these two intercepts and drawing a straight line through them.

Do you want more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How do you calculate the slope of a line between two points?
2. What is the general formula for slope-intercept form?
3. How does changing the slope \(m\) affect the graph of the line?
4. What is the significance of the y-intercept in real-world applications?
5. How would the graph change if the equation were \(y = -2x + 4\)?

**Tip**: Always check your intercepts by substituting them back into the original equation to verify their correctness.

Find the x-intercept and y-intercept of the equation y = -x + 4, and plot the graph.

Learn how to find the x-intercept and y-intercept of the linear equation y = -x + 4. This guide provides step-by-step calculations and explanations, along with graphing techniques suitable for students in Grades 7-10.

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