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 graph passes through the origin \((0,0)\) (since when \( x = 0 \), \( y=0\)).

Step2: Compare with given equation

The given equation is \( y = 5x \). Here, \( k = 5 \), which is a constant. Also, when \( x = 0 \), \( y=5\times0 = 0 \), so the graph passes through the origin. This matches the form of a proportional relationship.

Answer:

Yes, the equation \( y = 5x \) represents a proportional relationship. A proportional relationship is defined by an equation of the form \( y=kx \) (where \( k \) is a constant, called the constant of proportionality) and the graph passes through the origin \((0,0)\). For \( y = 5x \), \( k = 5 \) (a constant), and when \( x = 0 \), \( y=0 \), so it satisfies the conditions of a proportional relationship.