Final answer:
None of the provided equations (F. y = x - 1, G. y = x - 3, H. y = x + 5, I. y = 2x - 3) represents a direct variation because each one has a non-zero y-intercept, which disqualifies them from being in the form y = kx, where k is a constant and there is no y-intercept term.
Step-by-step explanation:
To determine which of the given equations represents a direct variation, we should look for an equation that can be written in the form y = kx, where k is a constant, and there is no y-intercept term (the b in y = mx + b should be zero). In direct variation, as x increases or decreases, y changes proportionally. The question provided contains four options, and we need to identify the one that fits the criteria for direct variation.
- F. y = x - 1: This equation has a y-intercept of -1, which disqualifies it as a direct variation.
- G. y = x - 3: This equation has a y-intercept of -3, which disqualifies it as a direct variation.
- H. y = x + 5: This equation has a y-intercept of 5, which disqualifies it as a direct variation.
- I. y = 2x - 3: This equation has a non-zero y-intercept of -3, which means it is not a direct variation.
In conclusion, none of the equations F, G, H, or I represents a direct variation because each one of them has a non-zero y-intercept.