Question

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

a) y =7×
b) y =9× c) y=x^2
d) y= 1/x
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Answer 1

Equations y = 7x and y = 9x exhibit a proportional relationship between x and y as they maintain a constant ratio, characteristic of direct proportionality.

Step-by-step explanation:

To determine which equations show a proportional relationship between x and y, we can recall that a proportional relationship is one in which the ratio y/x remains constant. This is represented by equations of the form y = kx, where k is the constant of proportionality. Looking at the given equations:

a) y = 7x: This shows a direct proportionality with a constant of 7.

b) y = 9x: Also shows a direct proportionality with a constant of 9.

c) y = x2: This is a quadratic relationship and is not proportional.

d) y = 1/x: This represents an inverse relationship, which is also not proportional.

Therefore, the equations y = 7x and y = 9x show a proportional relationship.