In a direct variation, as x increases, does y increase or decrease?
In a direct variation, as x increases, y also increases. This means that the variables x and y have a proportional relationship, where y is directly proportional to x.
To understand why this is the case, we need to look at the definition of direct variation. In mathematics, two variables are said to have a direct variation when their values are related by a constant ratio.
Mathematically, a direct variation can be expressed as the equation y = kx, where y and x are the variables, and k is the constant of variation. The constant k represents the ratio between the values of y and x.
So, when x increases, y will also increase because the constant k remains the same. This means that for every increase in x, there will be a corresponding increase in y.
To further clarify this concept, let's consider an example. Suppose we have a direct variation between the number of hours worked (x) and the amount of money earned (y). If the constant of variation is $10 per hour, then for every increase of 1 hour worked, the person would earn an additional $10. As the number of hours worked increases, the amount of money earned will also increase.
Therefore, in a direct variation, as x increases, y will also increase.
depends on the constant of variation.
y = kx
if k is positive, y increases
if k is negative, y decreases