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The given function is \( f(x) = 2x + 3 \), where the slope is \( 2 \) and the \( y \)-intercept is \( 3 \). The problem asks how the function changes if the \( y \)-intercept becomes \( -5 \).

### Analyzing the options:

1. **A.** "The graph of the line would be translated down 8 units."
   - This is **correct** because the \( y \)-intercept decreases from \( 3 \) to \( -5 \), which is a change of \( 8 \) units downward.

2. **B.** "The graph of the line would be translated up 8 units."
   - This is **incorrect** because the graph is moving downward, not upward.

3. **C.** "The slope of the line would change from increasing to decreasing."
   - This is **incorrect** because the slope does not change, it remains \( 2 \), which is positive, indicating the line is still increasing.

4. **D.** "The slope of the line would change from decreasing to increasing."
   - This is **incorrect** as the slope remains unchanged at \( 2 \).

5. **E.** "The function would become \( f(x) = -5x + 3 \)."
   - This is **incorrect** because the slope would have to change to \( -5 \), but we are only changing the \( y \)-intercept.

6. **F.** "The function would become \( f(x) = 2x - 5 \)."
   - This is **correct** because the slope stays \( 2 \), and the new \( y \)-intercept is \( -5 \), which gives the equation \( f(x) = 2x - 5 \).

### Correct answers: 
- **A** and **F**.

Would you like a more detailed explanation on any part of this? Here are some related questions:

1. What is the effect of changing the slope in a linear function?
2. How can you calculate the change in the graph's position given a change in the \( y \)-intercept?
3. Why does a change in the \( y \)-intercept not affect the slope?
4. How can you tell if a line is increasing or decreasing from its slope?
5. How would changing both the slope and the intercept affect the graph of the function?

**Tip**: In a linear function, the slope controls the steepness and direction of the line, while the \( y \)-intercept determines where it crosses the vertical axis.

How does the function f(x) = 2x + 3 change if the y-intercept is changed to -5?

Explore how changing the y-intercept of the function f(x) = 2x + 3 to -5 affects the graph. Understand the shift in the graph and why the slope remains unchanged. Perfect for Grades 8-10 algebra learners.

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