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

Select TWO correct answers.
A.The function would become f(x) = 2x – 5.
B.The slope of the line would change from increasing to decreasing.
C.The function would become f(x) = –5x + 3.
D.The graph of the line would be translated up 8 units.
E.The slope of the line would change from decreasing to increasing.
F.The graph of the line would be translated down 8 units.

The function given is \( f(x) = 2x + 3 \), where the slope is \( 2 \) and the y-intercept is \( 3 \). Changing the y-intercept to \( -5 \) means the function becomes:

\[
f(x) = 2x - 5
\]

This preserves the slope of the line, but changes the point where the line crosses the y-axis.

The two correct answers are:

1. **A**: The function would become \( f(x) = 2x - 5 \).
2. **F**: The graph of the line would be translated down 8 units (because \( 3 - (-5) = 8 \)).

### Explanation:
- The slope (2) remains the same, so the line still increases at the same rate.
- The only change is a shift downward on the y-axis by 8 units, from \( 3 \) to \( -5 \).

### Incorrect answers:
- **B** and **E**: The slope does not change; it remains positive (increasing).
- **C**: This equation changes the slope, which is incorrect.
- **D**: The line is translated **down**, not up.

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Would you like more details or have any questions?  
Here are 5 related questions:

1. How do you determine the slope and y-intercept from an equation?
2. What happens to a line's graph when only the slope is changed?
3. How do we translate a graph up or down algebraically?
4. What are other ways to interpret a linear function’s transformation?
5. How can you find the point where a line crosses the x-axis?

**Tip**: The slope of a line determines its steepness, while the y-intercept shows where it crosses the y-axis.

How does the function f(x) = 2x + 3 change if the y-intercept is changed to –5?
Select TWO correct answers.
A.The function would become f(x) = 2x – 5.
B.The slope of the line would change from increasing to decreasing.
C.The function would become f(x) = –5x + 3.
D.The graph of the line would be translated up 8 units.
E.The slope of the line would change from decreasing to increasing.
F.The graph of the line would be translated down 8 units.

Discover how changing the y-intercept of the linear function f(x) = 2x + 3 to -5 affects the graph. This problem explains how the function is transformed algebraically and graphically, covering key concepts such as slope, y-intercept, and graph translation. Suitable for students in Grades 8-10.

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