Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

What equation represents direct variation?

1. y = k/x

2. y = k

3. y = kx

4. y = x + k

The correct answer is: y = kx

The equation that represents direct variation is expressed as y = kx, where k is a non-zero constant. This relationship indicates that as one variable (x) increases or decreases, the other variable (y) changes in direct proportion. The constant k represents the ratio of y to x, showcasing that y varies directly with x. In a direct variation scenario, if you were to graph the equation, you'd find that it creates a straight line through the origin (0,0). This means that when x equals zero, y will also equal zero, reinforcing the idea that direct variation has that intrinsic relationship between the two variables. The other equations provided do not represent direct variation. For instance, y = k/x represents an inverse variation, where y decreases as x increases. The equation y = k has no variable component related to x, indicating a constant value of y regardless of changes in x. Lastly, y = x + k represents a linear relationship, but it does not demonstrate direct variation because the addition of k shifts the line vertically rather than directly proportional scaling with x. Thus, the clear representation of direct variation is encapsulated in y = kx.