To find the constant of proportionality from the points on the graph, we first need to define what the points represent. It appears that the points given are \((0, 0)\), \((3, y)\), and \((6, y)\). Without specific values for \(y\) at these points, let's assume the points correspond to a linear relationship.
If you have a proportional relationship of the form:
\[ y = kx \]
where \(k\) is the constant proportionality, we can use the points to find \(k\).
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At the point (0, y): If the point is (0,0), it doesn't help in finding \(k\).
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At the point (3, y): Assuming this point has a certain coordinate \((3, y)\), we can express it as: \[ y = k \cdot 3 \]
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At the point (6, y): Similarly, this point can be expressed as: \[ y = k \cdot 6 \]
Given the information from the graph with known points, if we assume \(y\) takes specific consistent values at these points, we could establish a relationship.
Now, let's check the constant proportionality of each option (A, B, C, D) from the fact that when \(x = 0\), \(y = 0\) (this is typical for proportional relationships), and then find \(k\) when you have specific values for \(y\).
For example, if for \(x = 3\), \(y = 2\), and for \(x = 6\), \(y = 4\): \[ k = \frac{y}{x} \]
- For (3,2): \(k = \frac{2}{3}\)
- For (6,4): \(k = \frac{4}{6} = \frac{2}{3}\)
Now checking the options given:
- A. \( \frac{3}{2} \)
- B. \( \frac{1}{2} \)
- C. \( 2 \)
- D. \( \frac{2}{3} \)
If each calculated \(k\) is consistent with D: \( \frac{2}{3} \), then that would be your answer.
So, the constant of proportionality from the graph is D. \( \frac{2}{3} \).