Question

select the equations that show a proportional relationship between x and y. y = 6x - 5 y = 10x

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 \(y = 6x - 5\)

Substitute \(x = 0\) into \(y = 6x - 5\), we get \(y = 6(0)-5=-5
eq0\). So it does not pass through the origin, hence not proportional.

Step3: Analyze \(y = 10x\)

Substitute \(x = 0\) into \(y = 10x\), we get \(y = 10(0) = 0\). It is in the form \(y=kx\) with \(k = 10\), so it is proportional.

Answer:

The equation that shows a proportional relationship between \(x\) and \(y\) is \(y = 10x\) (the second equation). The equation \(y=6x - 5\) does not show a proportional relationship.