Question

does the equation y = 5x represent a proportional relationship? explain your answer

Explanation:

Step1: Recall Proportional Relationship Form

A proportional relationship has the form \( y = kx \), where \( k \) is a constant (the constant of proportionality), and the line passes through the origin (\( x = 0, y = 0 \)).

Step2: Compare with Given Equation

The given equation is \( y = 5x \). Here, \( k = 5 \) (a constant), and when \( x = 0 \), \( y = 5(0)=0 \), so it passes through the origin. Thus, it matches the form of a proportional relationship.

Answer:

Yes, the equation \( y = 5x \) represents a proportional relationship. It is in the form \( y = kx \) (where \( k = 5 \), a constant), and when \( x = 0 \), \( y = 0 \), meaning the graph passes through the origin, which is a key characteristic of proportional relationships.