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.