y = 3 x equation represents a proportional relationship.
Answer: Option B
Step-by-step explanation:
A proportional variation represents a relationship between two variables x and y. It can be expressed in the form y=k x. Here, the ‘k’, the proportionality constant is equal to the slope m and the line goes through the origin
case A) [tex]y=2\left(x+\frac{1}{3}\right)[/tex]
A linear equation that not passes through the origin and so not proportional variation
case B) y= 3 x
Is a linear equation but passes through the origin and so proportional variation
case C) y = - 3x+2
A linear equation that not passes through the origin and so not proportional variation
case D) [tex]\text { D) } y=\frac{1}{2 x}[/tex]
An inverse variation equation but not passes through the origin and so not proportional variation.
From these, equation option B is the proportion equation because in these equations, there is no addition and subtraction of any constant number. That’s why both these equations become proportional equations.
