Question

select the equations that show a proportional relationship between x and y.
y = 9x
y = 6x
submit

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

Step2: Analyze \( y = 9x \)

For \( y = 9x \), when \( x = 0 \), \( y = 9(0)=0 \). It is in the form \( y = kx \) with \( k = 9 \), so it shows a proportional relationship.

Step3: Analyze \( y = 6x \)

For \( y = 6x \), when \( x = 0 \), \( y = 6(0)=0 \). It is in the form \( y = kx \) with \( k = 6 \), so it also shows a proportional relationship.

Answer:

The equations \( y = 9x \) and \( y = 6x \) show a proportional relationship between \( x \) and \( y \) (as they are in the form \( y = kx \) with \( k = 9 \) and \( k = 6 \) respectively, and satisfy the conditions for proportionality). So the selected equations \( y = 9x \) and \( y = 6x \) are correct.