Question

select the equations that show a proportional relationship between x and y.
☑️ y = 2x
☑️ y = 5x

Explanation:

Step1: Recall Proportional Relationship

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

Step2: Analyze \( y = 2x \)

For \( y = 2x \), comparing with \( y = kx \), we have \( k = 2 \) (a constant). When \( x = 0 \), \( y = 0 \), so it's a proportional relationship.

Step3: Analyze \( y = 5x \)

For \( y = 5x \), comparing with \( y = kx \), we have \( k = 5 \) (a constant). When \( x = 0 \), \( y = 0 \), so it's also a proportional relationship.

Answer:

The equations that show a proportional relationship between \( x \) and \( y \) are \( \boldsymbol{y = 2x} \) and \( \boldsymbol{y = 5x} \) (as both are in the form \( y = kx \) with constant \( k \) and pass through the origin).