The problem asks which of the given lines goes through the point $(0, 4)$ and is parallel to the line $y = 5x - 3$.

Key points:

1. Parallel lines have the same slope. The slope of the line $y = 5x - 3$ is 5 because it's in the form $y = mx + b$, where $m$ is the slope.

2. For the line to be parallel, it must also have a slope of 5. So, we are looking for an equation of the form $y = 5x + b$.

Check the equations provided:

• $y = 5x - 7$ has slope 5.
• $y = 5x + 4$ has slope 5.
• $y = -5x - 3$ has slope -5 (not parallel).

Next, we check which of these lines passes through the point $(0, 4)$.

• For $y = 5x - 7$, substituting $x = 0$ gives $y = -7$, which does not pass through $(0, 4)$.
• For $y = 5x + 4$, substituting $x = 0$ gives $y = 4$, which is correct.

Thus, the line $y = 5x + 4$ is parallel to $y = 5x - 3$ and passes through the point $(0, 4)$.

Final Answer: The correct line is $y = 5x + 4$.

Would you like more details or explanations on any part of this solution?

Here are 5 related questions to explore further:

1. What are the properties of parallel lines?
2. How do you determine if two lines are perpendicular instead of parallel?
3. Can two lines with different slopes ever be parallel?
4. How does the y-intercept affect the position of a line on a graph?
5. How would the answer change if the line was perpendicular instead of parallel?

Tip: When checking if a point lies on a line, always substitute the x- and y-values into the equation and verify the equality!