To graph the proportional relationship represented by the equation \( y = 2x \), we can create a set of points by choosing different values for \( x \) and calculating the corresponding \( y \) values.
Here are a few points we can plot:
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When \( x = 0 \): \[ y = 2(0) = 0 \quad \Rightarrow \quad (0, 0) \]
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When \( x = 1 \): \[ y = 2(1) = 2 \quad \Rightarrow \quad (1, 2) \]
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When \( x = 2 \): \[ y = 2(2) = 4 \quad \Rightarrow \quad (2, 4) \]
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When \( x = 3 \): \[ y = 2(3) = 6 \quad \Rightarrow \quad (3, 6) \]
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When \( x = -1 \): \[ y = 2(-1) = -2 \quad \Rightarrow \quad (-1, -2) \]
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When \( x = -2 \): \[ y = 2(-2) = -4 \quad \Rightarrow \quad (-2, -4) \]
Now, we can plot these points on a coordinate plane:
- (0, 0)
- (1, 2)
- (2, 4)
- (3, 6)
- (-1, -2)
- (-2, -4)
To draw the graph:
- Mark the points on grid paper or a graphing tool.
- Connect the points with a straight line, which will extend in both directions, indicating that they form a linear relationship.
The line should pass through the origin (0, 0) and have a positive slope, indicating a proportional relationship where \( y \) is always twice the value of \( x \).
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