To graph the proportional relationship described by the equation \( y = 2x \), we can calculate several points based on this equation by choosing different values for \( x \) and finding the corresponding \( y \):
- If \( x = 0 \), then \( y = 2(0) = 0 \) → point \( (0, 0) \)
- If \( x = 1 \), then \( y = 2(1) = 2 \) → point \( (1, 2) \)
- If \( x = 2 \), then \( y = 2(2) = 4 \) → point \( (2, 4) \)
- If \( x = 3 \), then \( y = 2(3) = 6 \) → point \( (3, 6) \)
- If \( x = 4 \), then \( y = 2(4) = 8 \) → point \( (4, 8) \)
Now, we can plot the points on a coordinate plane:
- \( (0, 0) \)
- \( (1, 2) \)
- \( (2, 4) \)
- \( (3, 6) \)
- \( (4, 8) \)
From the options given, the correct one that matches our calculated points is:
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 reflects the relationship \( y = 2x \) accurately with the points plotted correctly.