Question

select the equations that show a proportional relationship between x and y.
y = 3x y = 7x - 1
submit

Explanation:

Step1: Recall proportional relationship

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

Step2: Analyze \(y = 3x\)

For \(y = 3x\), when \(x = 0\), \(y = 3(0)=0\). It is in the form \(y = kx\) with \(k = 3\), so it is proportional.

Step3: Analyze \(y = 7x - 1\)

For \(y = 7x - 1\), when \(x = 0\), \(y = 7(0)-1=- 1
eq0\). It is a linear equation but not in the form \(y = kx\) (it has a y - intercept of \(-1\)), so it is not proportional.

Answer:

Only \(y = 3x\) shows a proportional relationship between \(x\) and \(y\). So the correct equation is \(y = 3x\).