A proportional relationship is represented by a linear graph that passes through the origin (0, 0). This means that the line must have a y-intercept of 0.
Let's evaluate the options:
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A graph of a line that passes through the points (0, 0) and (1, -3): This line starts at the origin, but since the second point is not above the x-axis, it does not represent a proportional relationship. The slope is negative, and the y-values are not proportional to the x-values.
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A graph of a line that passes through the points (0, 2) and (1, 2): This line is horizontal and doesn't pass through the origin. It represents a constant value (y = 2), not a proportional relationship.
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A graph of a line that passes through the points (0, -3) and (2, 1): This line does not pass through the origin (it starts at -3 on the y-axis), and therefore does not represent a proportional relationship.
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A graph of a line that passes through the points (0, -1) and (2, -2): This line also does not pass through the origin (it starts at -1 on the y-axis) and does not represent a proportional relationship.
None of the options provided represent a proportional relationship since none of them pass through the origin (0,0).