Question 5

y=2x+2 expresses a relationship between x and y.

The equation y=2x+2 accurately describes a linear relationship where y increases by 2 for every unit increase in x, indicating a consistent rate of change.

A) y=x+2

This option suggests that for every unit increase in x, y increases by 1, which does not match the relationship expressed in the correct answer. Therefore, it fails to represent the appropriate correlation between x and y.

B) y=2x

While this equation represents a direct proportionality where y doubles with each unit increase in x, it lacks the constant term that shifts the line vertically. Thus, it doesn't match the relationship defined by the correct answer.

C) y=2x+2

This equation effectively captures the relationship between x and y, indicating that y not only scales with x but also has a vertical shift of 2 units. This makes it the correct expression of their relationship.

D) y=3x+2

This option indicates that y increases by 3 for every unit increase in x, which is inconsistent with the correct answer. The incorrect rate of change disqualifies it from expressing the appropriate relationship.

Conclusion

The equation y=2x+2 is the only option that accurately reflects the linear relationship between x and y, incorporating both a proper slope and a vertical shift. The other options either misrepresent the rate of change or lack the necessary constant to align with the relationship described.