Test of Essential Academic Skills (TEAS) ATI Mathematics Practice Test

Using a given chart, which equation describes the relationship between x and y?

1. x = 3y

2. y = 3x

3. y = 1/3x

4. x/y = 3

The correct answer is: y = 3x

To understand why the equation y = 3x is appropriate for the relationship between x and y based on the given chart, it is essential to consider how the two variables relate to each other. In this case, if the y-values increase as the x-values increase and the change in y is three times that of x, this indicates a proportional relationship where y is directly proportional to x with a constant of proportionality equal to 3. When graphed, this relationship is a straight line that passes through the origin (0,0), indicating that at x = 0, y will also be 0. The slope of the line is 3, meaning for every one unit increase in x, y increases by three units. This consistent ratio confirms that y can indeed be expressed as three times the value of x. In contrast, the other equations do not accurately capture this relationship. For instance, if we were to analyze the equation in D (x/y = 3), it implies a constant ratio of 3 between x and y, which could potentially be misinterpreted without recognizing the context of proportional growth. However, the simple and direct relationship described by y = 3x provides a clearer and more straightforward understanding of how y responds