Final answer:
The graph that represents a function with direct variation is the one with a line passing through (-2, 1), (0, 0), and (2, -1), which indicates a straight line with a constant negative slope that passes through the origin.
Step-by-step explanation:
The graph that represents a function with direct variation is described by the equation y = mx, where m is a constant representing the slope of the line. In direct variation, there is no y-intercept, which means the line must pass through the origin (0,0). Reviewing the options given:
- A coordinate grid with a line passing through (0, 1) and (1, 1) is a horizontal line and does not represent direct variation.
- A coordinate grid with a line passing through (negative 2, 1), (0, 0) and (2, negative 1) does represent direct variation since it passes through the origin and has a constant negative slope.
- A coordinate grid with a line passing through (negative 3, negative 3), (0, negative 2) and (3, negative 1) does not pass through the origin, so it does not represent direct variation.
- A coordinate grid with a line passing through (negative 2, negative 2), (0, 1) and (2, 4) does not pass through the origin, so it also does not represent direct variation.
The correct answer is a graph with a line passing through (negative 2, 1), (0, 0) and (2, negative 1), indicating it is a straight line with a negative slope and passes through the origin, which fits the criteria for direct variation.