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.