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Graph the proportional relationship y=−2x

by plotting points.(1 point)
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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 the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma negative 2 right parenthesis, and left parenthesis 2 comma negative 4 right parenthesis.
Image with alt text: 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 the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma negative 2 right parenthesis, and left parenthesis 2 comma negative 4 right parenthesis.

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 the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 2 right parenthesis, and left parenthesis 2 comma 4 right parenthesis.
Image with alt text: 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 the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 2 right parenthesis, and left parenthesis 2 comma 4 right parenthesis.

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 the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma negative 1 right parenthesis, and left parenthesis 2 comma negative 2 right parenthesis.
Image with alt text: 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 the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma negative 1 right parenthesis, and left parenthesis 2 comma negative 2 right parenthesis.

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 the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 5 right parenthesis, and left parenthesis 2 comma 10 right parenthesis.
Image with alt text: 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 the ends joins three plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 5 right parenthesis, and left parenthesis 2 comma 10 right parenthesis.
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1 answer

To determine the correct graph for the proportional relationship given by the equation \( y = -2x \), let's analyze the equation and calculate a few points.

  1. Plugging in values for \( x \):

    • When \( x = 0 \): \[ y = -2(0) = 0 \quad \Rightarrow \quad (0, 0) \]
    • When \( x = 1 \): \[ y = -2(1) = -2 \quad \Rightarrow \quad (1, -2) \]
    • When \( x = 2 \): \[ y = -2(2) = -4 \quad \Rightarrow \quad (2, -4) \]
    • When \( x = -1 \): \[ y = -2(-1) = 2 \quad \Rightarrow \quad (-1, 2) \]

  2. Identifying the plotted points:

    • The key points we calculated are:
      • \( (0, 0) \)
      • \( (1, -2) \)
      • \( (2, -4) \)

Given the options:

  • The first option has the points \( (0, 0) \), \( (1, -2) \), and \( (2, -4) \), which corresponds correctly to \( y = -2x \).
  • The other options involve incorrect points based on the equation given.

Therefore, the correct graph corresponds to the first image where the plotted points are \( (0, 0) \), \( (1, -2) \), and \( (2, -4) \). This graph depicts the line representing the equation \( y = -2x \), which is a downward-sloping line through the origin.