Final answer:
None of the given equations A. y = x - 1, B. y = x 3 (presumed typo), C. y = x + 5, or D. y = 2x - 3 represent a direct variation because each one has a non-zero y-intercept. Direct variation should be in the form y = mx with no y-intercept.
Step-by-step explanation:
The student is asking which of the given equations represents a direct variation. A direct variation is a special type of linear equation where the ratio of the dependent variable (y) to the independent variable (x) is constant. This ratio is the slope of the line, and in a direct variation, there is no y-intercept (b = 0 in the equation y = mx + b).
Looking at the given options, we can analyze each to determine if they fit the criteria for direct variation:
- A. y = x - 1 has a y-intercept of -1, so it is not a direct variation.
- B. y = x 3 seems to be a typo, but if it means y = x + 3, it also has a y-intercept of 3, so it is not a direct variation.
- C. y = x + 5 also has a y-intercept of 5, therefore it is not a direct variation.
- D. y = 2x - 3, the y-intercept is -3, so this too is not a direct variation.
However, none of the presented options strictly adhere to the requirements for direct variation as they all have non-zero y-intercepts. Therefore, based on the concept of direct variation, where the equation should have the form y = mx, none of the options A through D represent a direct variation. If we had to select the one that most closely represents direct variation, we would typically look for the equation with no constant term (no y-intercept), but since all have a y-intercept, there is no correct answer given in the options.