Question

Graph the proportional relationship y = 2x by plotting points
A. (0,0) (1,3) (2,6)
B. (0,0) (1,4)
C. (0,0) (2,1)
D. (0,0) (1,2) (2,4)

Answer 1

To determine which set of points represents the proportional relationship \(y = 2x\), we can substitute the x-values into the equation and see if the resulting y-values match the ones given in the options.

1. **For \(x = 0\)**:
\[ y = 2(0) = 0 \]
Thus the point is \( (0, 0) \).

2. **For \(x = 1\)**:
\[ y = 2(1) = 2 \]
Thus the point is \( (1, 2) \).

3. **For \(x = 2\)**:
\[ y = 2(2) = 4 \]
Thus the point is \( (2, 4) \).

So we have the points \( (0, 0) \), \( (1, 2) \), and \( (2, 4) \).

Now let's evaluate the options:

A. **(0,0) (1,3) (2,6)**
- \( (1, 3) \): Incorrect, since \(2(1) = 2\), not 3.
- \( (2, 6) \): Incorrect, since \(2(2) = 4\), not 6.

B. **(0,0) (1,4)**
- \( (1, 4) \): Incorrect, since \(2(1) = 2\), not 4.

C. **(0,0) (2,1)**
- \( (2, 1) \): Incorrect, since \(2(2) = 4\), not 1.

D. **(0,0) (1,2) (2,4)**
- \( (1, 2) \): Correct, since \(2(1) = 2\).
- \( (2, 4) \): Correct, since \(2(2) = 4\).

Thus, the correct option representing the proportional relationship \(y = 2x\) by plotting points is **D**: (0,0), (1,2), (2,4).