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:
-
Graft 1: (0, 0), (2, 1)
- Does not satisfy \(y = 2z\) as \(y\) should be 4 when \(z = 2\).
-
Graft 2: (0, 0), (1, 4)
- Does not satisfy \(y = 2z\) as \(y\) should be 2 when \(z = 1\).
-
Graft 3: (0, 0), (1, 3), (2, 6)
- Does not satisfy \(y = 2z\) as \(y\) should be 2 when \(z = 1\).
-
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.