Decide which of the following equations represents a proportional relationship.(1 point)

Question

Responses

y=3x+1
y equals 3 x plus 1

y=x/3−3
y equals Start Fraction x over 3 End Fraction minus 3

y=x+3
y equals x plus 3

y=1/3x

Answer 1

A proportional relationship can be identified by the form \(y = kx\), where \(k\) is a constant and there is no y-intercept (the equation passes through the origin).

Among the given equations, the only one that fits this criterion is:

\(y = \frac{1}{3}x\)

The other equations have a constant added or subtracted to \(x\) (indicating they do not pass through the origin), and therefore do not represent proportional relationships.

So, the correct answer is:

y = \frac{1}{3}x