https://file.aiquickdraw.com/mathbot/file/1726441070708iz84ln0b.jpg

Let's analyze the functions in the image and address the question:

There are four functions displayed:
1. **Function 1:** A graph with a line crossing the y-axis.
2. **Function 2:** A table with points for the linear function.
3. **Function 3:** The equation \( y = 4x + 3 \).
4. **Function 4:** Described as having a slope of -5 and a y-intercept of 5.

### Question:
- **(a) Which function has the graph with a y-intercept closest to 0?**

#### Solution:
We need to determine the y-intercept of each function.

1. **Function 1** (Graph): From the graph, it seems the line crosses the y-axis around -1, making the y-intercept close to -1.
2. **Function 2** (Table): To find the y-intercept, observe the table. When \( x = 0 \), \( y = -4 \). Thus, the y-intercept is -4.
3. **Function 3** (Equation \( y = 4x + 3 \)): The y-intercept is the constant term, which is 3.
4. **Function 4** (Given slope -5, y-intercept 5): The y-intercept is explicitly given as 5.

### Conclusion:
- **Function 1** has the y-intercept closest to 0, since its y-intercept is around -1.

Let me know if you want further clarification!

### Related Questions:
1. How do you calculate the slope from a graph or table of points?
2. What is the general formula for a linear equation, and how do you identify the slope and y-intercept?
3. How would you graph a function like \( y = -5x + 5 \) based on its slope and y-intercept?
4. Can a linear function have more than one y-intercept? Why or why not?
5. What is the significance of the slope in a real-world context, such as speed or rates?

### Tip:
To quickly find the y-intercept from a table, look for the value of \( y \) when \( x = 0 \).

Which function has the graph with a y-intercept closest to 0?

Compare four different linear functions to determine which has the y-intercept closest to 0. This problem involves analyzing graphs, tables, and equations, covering key concepts such as the slope-intercept form and graphing functions. Suitable for students in Grades 8-10.

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