To graph the propositional relationship \( y = 2x \), we can start by plotting a few points using different values of \( x \) and calculating the corresponding \( y \) values. The equation means that for every unit increase in \( x \), \( y \) increases by 2.
Here are some points we can calculate:
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When \( x = 0 \): \[ y = 2(0) = 0 \quad \text{(Point: (0, 0))} \]
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When \( x = 1 \): \[ y = 2(1) = 2 \quad \text{(Point: (1, 2))} \]
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When \( x = 2 \): \[ y = 2(2) = 4 \quad \text{(Point: (2, 4))} \]
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When \( x = 3 \): \[ y = 2(3) = 6 \quad \text{(Point: (3, 6))} \]
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When \( x = -1 \): \[ y = 2(-1) = -2 \quad \text{(Point: (-1, -2))} \]
Now, we can plot the points we calculated:
- (0, 0)
- (1, 2)
- (2, 4)
- (3, 6)
- (-1, -2)
You mentioned the dot (1, 4). Please note that the correct point for \( x = 1 \) in the equation \( y = 2x \) is (1, 2), not (1, 4).
Now, plot the points on a coordinate system and draw a straight line through them to represent the equation \( y = 2x \):
- (0, 0)
- (1, 2)
- (2, 4)
- (3, 6)
- (-1, -2)
The graph will show a straight line passing through these points, with a slope of 2. Be sure to draw the line extending in both directions as this is a linear function.
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