Question

Graph the proportional relationship y = 2z by plotting points. (1 point)
Given
graft 1 (0, 0) (2, 1)
graft 2 (0, 0) (1, 4)
graft 3 (0, 0) (1, 3) (2, 6)
graft 4 (0, 0) (1, 2) (2, 4)

Answer 1

To graph the proportional relationship \(y = 2z\), we need to plot some points based on this equation. In this case, \(y\) is double the value of \(z\).

**Calculating points:**
Let's calculate a few points (where \(z\) can take values 0, 1, 2, and 3):
- If \(z = 0\), then \(y = 2(0) = 0\) → point (0, 0)
- If \(z = 1\), then \(y = 2(1) = 2\) → point (1, 2)
- If \(z = 2\), then \(y = 2(2) = 4\) → point (2, 4)
- If \(z = 3\), then \(y = 2(3) = 6\) → point (3, 6)

**Points to plot:**
Thus, the points we can plot are:
- (0, 0)
- (1, 2)
- (2, 4)
- (3, 6)

Next, we will check which of the provided given grafts match the calculated points.

### Checking the given grafts:
1. **Graft 1:** (0, 0), (2, 1)
- Does not satisfy \(y = 2z\) as \(y\) should be 4 when \(z = 2\).

2. **Graft 2:** (0, 0), (1, 4)
- Does not satisfy \(y = 2z\) as \(y\) should be 2 when \(z = 1\).

3. **Graft 3:** (0, 0), (1, 3), (2, 6)
- Does not satisfy \(y = 2z\) as \(y\) should be 2 when \(z = 1\).

4. **Graft 4:** (0, 0), (1, 2), (2, 4)
- Matches \(y = 2z\) since (1, 2) corresponds to \(y=2(1)\) and (2, 4) corresponds to \(y=2(2)\).

### Conclusion:
The correct graph for the proportional relationship \(y = 2z\) among the given grafts is **Graft 4**: (0, 0), (1, 2), (2, 4).

You can plot these points on a coordinate plane, and they will lie on a straight line that goes through the origin (0, 0) with a slope of 2, indicating it's a proportional relationship.