Graph the proportional relationship y=−2x

Question

by plotting points.(1 point)
Responses

1;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.

2: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.

3: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.

4: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.
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Answer 1

To graph the proportional relationship given by the equation \( y = -2x \), we can calculate a few points that satisfy this equation:

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

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

3. When \( x = 2 \): \[ y = -2(2) = -4 \quad \Rightarrow \quad (2, -4) \]

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

5. When \( x = -2 \): \[ y = -2(-2) = 4 \quad \Rightarrow \quad (-2, 4) \]

Now, let’s analyze which of the provided options includes points that satisfy this equation. The relevant points should include the plotted coordinates (0, 0), (1, -2), and (2, -4).

From the given choices:

1. Option 1: Contains the points (0, 0), (1, -1), and (2, -2) — Not correct.
2. Option 2: Contains (0, 0), (1, 5), and (2, 10) — Not correct.
3. Option 3: Contains (0, 0), (1, -2), and (2, -4) — Correct.
4. Option 4: Contains (0, 0), (1, 2), and (2, 4) — Not correct.

Thus, the correct response that graphs the proportional relationship \( y = -2x \) is Option 3: A coordinate plane that includes the points (0, 0), (1, -2), and (2, -4).