If two quantities are proportional, the following statements must be true of a graph showing the relationship between them:
C. The graph increases from left to right.
D. The points of the graph form a straight line.
E. The points of the graph must include the origin.
F. The points must all form equivalent ratios.
Let's break it down:
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C: When one quantity increases, the other also increases, which generally leads to the graph rising from left to right.
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D: Proportional relationships are linear, meaning they form a straight line when graphed.
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E: A proportional relationship that passes through the origin means that if one quantity is zero, the other will also be zero (i.e., \(y = kx\) where \(k\) is a constant).
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F: Proportionality means all points on the graph represent equivalent ratios of the two quantities.
A (The graph is a curve) is false for a proportional relationship since it is linear.
B (The points on the graph are connected) is not necessarily true for discrete data points, though the relationship is still linear.
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