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The worksheet asks you to find the **x-intercept** and **y-intercept** of several linear functions and graphs. Let’s go over each one step-by-step.

### Top Left:
For the **graph**, observe where the line crosses the x-axis and y-axis:
- **x-intercept**: This is the point where the line crosses the x-axis. The x-intercept occurs where \( y = 0 \).
- **y-intercept**: This is the point where the line crosses the y-axis. The y-intercept occurs where \( x = 0 \).

### Top Right (Graph):
- **x-intercept**: Looking at the graph, the line crosses the x-axis at \( (6, 0) \).
- **y-intercept**: The line crosses the y-axis at \( (0, 4) \).

### Middle Left: \( f(x) = x - 3 \)
This is a linear equation in slope-intercept form, \( f(x) = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
- **y-intercept**: The y-intercept occurs at \( b = -3 \), so the y-intercept is \( (0, -3) \).
- **x-intercept**: To find the x-intercept, set \( f(x) = 0 \):
  \[
  x - 3 = 0 \implies x = 3
  \]
  So the x-intercept is \( (3, 0) \).

### Middle Right: \( f(x) = 2x + 4 \)
- **y-intercept**: The y-intercept is \( b = 4 \), so it’s \( (0, 4) \).
- **x-intercept**: Set \( f(x) = 0 \):
  \[
  2x + 4 = 0 \implies 2x = -4 \implies x = -2
  \]
  So the x-intercept is \( (-2, 0) \).

### Bottom Left: \( f(x) = -3x - 12 \)
- **y-intercept**: The y-intercept is \( b = -12 \), so it’s \( (0, -12) \).
- **x-intercept**: Set \( f(x) = 0 \):
  \[
  -3x - 12 = 0 \implies -3x = 12 \implies x = -4
  \]
  So the x-intercept is \( (-4, 0) \).

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Would you like a further breakdown of any part? Here are five follow-up questions to consider:

1. How do you find intercepts for nonlinear functions?
2. Can the x-intercept and y-intercept be the same point?
3. What is the geometric interpretation of the slope in these functions?
4. How do you determine intercepts graphically versus algebraically?
5. How would these steps change if the equation were quadratic instead of linear?

**Tip**: When finding intercepts, always remember that the x-intercept occurs where \( y = 0 \), and the y-intercept occurs where \( x = 0 \).

Find the x-intercept and y-intercept of the given functions and graphs.

Learn how to find the x-intercept and y-intercept of various linear functions, both from equations and graphs. This worksheet covers key algebra concepts such as graphing, slope-intercept form, and solving for intercepts. Suitable for students in Grades 7-10.

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