Bot GPT 4-o mini To graph the proportional relationship represented by the equation \( y = 2x \), we can plot several points that satisfy this equation. A proportional relationship means that as one quantity increases, the other quantity increases at a constant rate.
Steps to Plot Points:
- Choose Values for \( x \): Select a few values for \( x \).
- Calculate Corresponding \( y \) Values: Use the equation \( y = 2x \) to calculate \( y \) for each chosen value of \( x \).
- Plot Points: Plot the resulting points on a Cartesian coordinate system (xy-plane).
- Draw the Line: Since this is a linear equation, draw a straight line through the plotted points.
Example Points:
Let's choose the following values for \( x \): -2, -1, 0, 1, 2.
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For \( x = -2 \): \[ y = 2(-2) = -4 \quad \Rightarrow (-2, -4) \]
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For \( x = -1 \): \[ y = 2(-1) = -2 \quad \Rightarrow (-1, -2) \]
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For \( x = 0 \): \[ y = 2(0) = 0 \quad \Rightarrow (0, 0) \]
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For \( x = 1 \): \[ y = 2(1) = 2 \quad \Rightarrow (1, 2) \]
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For \( x = 2 \): \[ y = 2(2) = 4 \quad \Rightarrow (2, 4) \]
List of Points to Plot:
- (-2, -4)
- (-1, -2)
- (0, 0)
- (1, 2)
- (2, 4)
Graphing:
After calculating and plotting these points, you would see that they form a straight line through the origin (0,0). The slope of the line is 2, indicating that for every unit increase in \( x \), \( y \) increases by 2 units.
Conclusion:
The line represents a proportional relationship between \( x \) and \( y \), confirming that the equation \( y = 2x \) is indeed a linear relationship that goes through the origin. You can graph this on graph paper or using graphing software to visualize it clearly.
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