Question
Decide which of the following equations represents a proportional relationship.(1 point)
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
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
Answers
GPT-4o mini
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**
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**