https://r2.erweima.ai/mathbot/image/1724674584956xxzng03h.jpg

https://r2.erweima.ai/mathbot/image/1724674584957smkc6r4i.jpg

daas sind 3 graphen und dazu die möglichen gleichungen 

To match the graphs to their corresponding equations, let's analyze the properties of the graphs and the equations given:

### Analysis of Graphs:
1. **Graph (a):**
   - The line passes through the origin (0, 0).
   - It has a positive slope, meaning as \( x \) increases, \( y \) increases.

2. **Graph (b):**
   - The line also passes through the origin (0, 0).
   - It has a negative slope, meaning as \( x \) increases, \( y \) decreases.

3. **Graph (c):**
   - This is a horizontal line, which indicates a constant \( y \) value regardless of \( x \).

### Analysis of Equations:
1. **\( y = -\frac{x}{2} \)** - This is a linear equation with a negative slope of \( -\frac{1}{2} \).
2. **\( y = 2x - 2 \)** - A linear equation with a slope of 2 and a y-intercept at \( -2 \).
3. **\( y = 2 - 2x \)** - This is equivalent to \( y = -2x + 2 \), a linear equation with a negative slope of \( -2 \).
4. **\( y = 1 \)** - A constant function where \( y = 1 \) regardless of \( x \).
5. **\( y = 1.5x \)** - A linear equation with a positive slope of 1.5.
6. **\( y = x \)** - A linear equation with a slope of 1.
7. **\( y = -0.5 \)** - A constant function where \( y = -0.5 \) regardless of \( x \).

### Matching:
- **Graph (a):** This graph has a positive slope. The correct equation is \( y = 1.5x \).
- **Graph (b):** This graph has a negative slope. The correct equation is \( y = -\frac{x}{2} \).
- **Graph (c):** This is a horizontal line, so the equation must be a constant. The correct equation is \( y = 1 \).

### Conclusion:
- **Graph (a) corresponds to \( y = 1.5x \).**
- **Graph (b) corresponds to \( y = -\frac{x}{2} \).**
- **Graph (c) corresponds to \( y = 1 \).**

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. What happens to the graph of a linear equation when the slope is increased?
2. How can you determine the slope of a line from its graph?
3. How do parallel lines on a graph relate to their slopes?
4. What does the y-intercept tell you about a linear equation?
5. How would you graph the equation \( y = 2x - 2 \) from the list?

**Tip:** The slope of a line is a measure of its steepness and is calculated as the ratio of the change in \( y \) to the change in \( x \).

Learn how to analyze graphs and match them to corresponding linear equations. This problem involves identifying slopes, intercepts, and graph characteristics. Suitable for students in Grades 7-9.

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