Which equation represents a direct variation?
A y = 5x
B y = 5/x
C y = 5
D y = 5 − x
The answer is A because direct variation has the equation y=KX
The equation that represents a direct variation is A. y = 5x. In a direct variation, when x increases, y also increases, and when x decreases, y also decreases. The equation y = 5x clearly shows this relationship as y is directly proportional to x, with a constant ratio of 5.
To determine which equation represents a direct variation, we need to understand what direct variation means. In mathematics, direct variation refers to a relationship where two variables are directly proportional to each other.
In a direct variation, if one variable increases, the other variable also increases by the same factor, or if one variable decreases, the other variable also decreases by the same factor.
Let's consider each option and analyze whether it represents a direct variation:
A) y = 5x: This equation represents a direct variation because y is directly proportional to x. As x increases, y increases at the same rate, given a constant ratio of 5.
B) y = 5/x: This equation does not represent a direct variation because y is inversely proportional to x. As x increases, y decreases, and vice versa.
C) y = 5: This equation represents a special case where y is constant, regardless of the value of x. It does not represent a direct variation.
D) y = 5 - x: This equation does not represent a direct variation because y and x are not directly proportional. When x increases, y decreases, but the rate of decrease is not constant.
Therefore, the equation that represents a direct variation is A) y = 5x.