Graph the proportional relationship y=2x

by plotting points.(1 point)
Responses

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 two plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis and left parenthesis 1 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 two plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis and left parenthesis 1 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 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 3 right parenthesis, and left parenthesis 2 comma 6 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 3 right parenthesis, and left parenthesis 2 comma 6 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 two plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis and left parenthesis 2 comma 1 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 two plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis and left parenthesis 2 comma 1 right parenthesis.

1 answer

To graph the proportional relationship given by the equation \( y = 2x \), we need to plot points based on this equation. The relationship indicates that for each unit increase in \( x \), \( y \) increases by a factor of 2.

Here are some points we can derive from the equation \( y = 2x \):

  1. When \( x = 0 \), \( y = 2(0) = 0 \) → Point (0, 0)
  2. When \( x = 1 \), \( y = 2(1) = 2 \) → Point (1, 2)
  3. When \( x = 2 \), \( y = 2(2) = 4 \) → Point (2, 4)
  4. When \( x = -1 \), \( y = 2(-1) = -2 \) → Point (-1, -2)
  5. When \( x = -2 \), \( y = 2(-2) = -4 \) → Point (-2, -4)

Therefore, the plotted points are (0, 0), (1, 2), and (2, 4).

Among the provided responses, the correct one includes these points:

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 shows the line representing the relationship \( y = 2x \).