Question

select the equations that show a proportional relationship between x and y.

☑️ ( y = x ) ☑️ ( y = 10x )

submit

Explanation:

Step1: Recall proportional relationship form

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

Step2: Analyze \(y = x\)

For \(y=x\), we can rewrite it as \(y = 1\times x\), where \(k = 1\) (a constant). When \(x = 0\), \(y = 0\), so it satisfies the proportional relationship form.

Step3: Analyze \(y = 10x\)

For \(y = 10x\), here \(k=10\) (a constant). When \(x = 0\), \(y = 0\), so it also satisfies the proportional relationship form \(y=kx\).

Answer:

The equations \(y = x\) and \(y=10x\) show a proportional relationship between \(x\) and \(y\) (since they are in the form \(y = kx\) with \(k = 1\) and \(k = 10\) respectively, and pass through the origin). So the selected equations are correct.