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

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

The original function is \( f(x) = 2x + 3 \), which has a slope of 2 and a y-intercept of 3. Changing the y-intercept to –5 only affects the constant term in the function, not the slope. Therefore, the new function would be \( f(x) = 2x - 5 \).

Let's analyze the options:

- **A.** The graph would be translated down 8 units: **Correct**. The y-intercept changes from 3 to –5, meaning the graph is translated downward by \( 3 - (-5) = 8 \) units.
- **B.** The graph would be translated up 8 units: **Incorrect**. The graph moves down, not up.
- **C.** The slope would change from increasing to decreasing: **Incorrect**. The slope remains the same (2), which is positive, so the function remains increasing.
- **D.** The slope would change from decreasing to increasing: **Incorrect**. The slope was always increasing and does not change.
- **E.** The function would become \( f(x) = -5x + 3 \): **Incorrect**. This changes the slope, which is not the case.
- **F.** The function would become \( f(x) = 2x - 5 \): **Correct**. This reflects the new y-intercept of –5.

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

Would you like further clarification on this problem or any of the concepts?

Here are 5 related questions:
1. How does changing the slope affect the graph of a linear function?
2. What is the slope of a horizontal line, and why?
3. How do you calculate the y-intercept of a linear function from an equation?
4. What happens to a graph when the slope is negative instead of positive?
5. How do you translate a linear graph vertically or horizontally?

**Tip**: When a linear function's y-intercept changes, only the vertical position of the graph shifts—slope remains unaffected.

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

Explore how changing the y-intercept of the linear function f(x) = 2x + 3 affects its graph. Learn how the graph is translated down 8 units when the y-intercept changes to -5, and the new function becomes f(x) = 2x - 5. Suitable for Grades 7-10.

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