Question

which equation represents a proportional relationship?
y = 4x + 1
y = 4x
y = x - 4
y = x + 4

Explanation:

Step1: Recall Proportional Relationship

A proportional relationship has the form \( y = kx \), where \( k \) is a constant (no constant term added or subtracted).

Step2: Analyze Each Equation

• For \( y = 4x + 1 \): Has a constant term \( +1 \), not proportional.
• For \( y = 4x \): Matches \( y = kx \) with \( k = 4 \), proportional.
• For \( y = x - 4 \): Has a constant term \( -4 \), not proportional.
• For \( y = x + 4 \): Has a constant term \( +4 \), not proportional.

Answer:

\( y = 4x \) (the second option)