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To determine which equation represents a proportional relationship, we must recall that in a proportional relationship, the equation takes the form:

\[
y = kx
\]

where \(k\) is a constant. The key characteristic of such a relationship is that the graph passes through the origin (0,0), meaning there is no constant term added or subtracted.

Let’s analyze the options:

1. \( y = x + 1 \) → Not proportional (it has a constant term +1).
2. \( y = 3x + 3 \) → Not proportional (it has a constant term +3).
3. \( y = 4x \) → Proportional (no constant term, just \(y = kx\) where \(k = 4\)).
4. \( y = 8 + x \) → Not proportional (constant term +8).

Thus, **\( y = 4x \)** represents a proportional relationship.

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. What is the proportional constant in the equation \( y = 5x \)?
2. How does the graph of a proportional relationship differ from a non-proportional one?
3. Can an equation of the form \( y = mx + b \) ever be proportional? Why or why not?
4. What would the graph of \( y = 4x \) look like?
5. How do you determine if a set of points represents a proportional relationship?

**Tip:** A proportional relationship always passes through the origin (0,0), as it has no constant term.

Which equation represents a proportional relationship?

Learn how to identify proportional relationships in equations. Explore key algebraic concepts such as linear equations and proportionality. Suitable for students in Grades 6-8.

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