To graph the propositional relationship \( y = 2x \), we can plot points by substituting values for \( x \) and calculating the corresponding \( y \) values.
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For \( x = 0 \): \[ y = 2(0) = 0 \quad \text{(Point: (0,0))} \]
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For \( x = 1 \): \[ y = 2(1) = 2 \quad \text{(Point: (1,2))} \]
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For \( x = 2 \): \[ y = 2(2) = 4 \quad \text{(Point: (2,4))} \]
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For \( x = 3 \): \[ y = 2(3) = 6 \quad \text{(Point: (3,6))} \]
Now we can compare these calculated points with the options provided:
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Option 1: Graph one Dot (1,4) - Incorrect, since \( y \) when \( x = 1 \) should be 2.
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Option 2: Graph 2 Dot 1 (1,3) Dot 2 (2,6) - Incorrect, as the correct values are \( (1,2) \) and \( (2,4) \).
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Option 3: Graph 3 Dot 1 (2,1) - Incorrect, since \( y \) when \( x = 2 \) is 4.
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Option 4: Graph 4 Dot 1 (1,2) Dot 2 (2,4) - Correct! The points plotted here match the function.
Therefore, the correct option to represent the relationship \( y = 2x \) by plotting points is Option 4: Dot 1 (1,2) and Dot 2 (2,4).