To graph the proportional relationship given by the equation \( y = -2x \), we can plot several points where \( x \) takes on different values, and subsequently, we can determine the corresponding \( y \) values.
For the equation \( y = -2x \), the points can be calculated as follows:
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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 \( x = 2 \): \[ y = -2(2) = -4 \quad \Rightarrow \quad (2, -4) \]
Now, we can summarize the points we have calculated:
- \( (0, 0) \)
- \( (1, -2) \)
- \( (2, -4) \)
From your options, the points:
- \( (0, 0) \)
- \( (1, -2) \)
- \( (2, -4) \)
match the third response: A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both ends joins three plotted points and extends beyond. The coordinates of the plotted points are: \( (0, 0) \), \( (1, -2) \), and \( (2, -4) \).
This is the correct graph representation of the relationship \( y = -2x \).