To determine if the given points (0, 3) and (5, 1) lie on the graph of the function \( y = \frac{2}{3}x + 3 \), we can plug in the x-values of each point into the equation and see if we get the corresponding y-values.
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For the point (0, 3):
- Substitute \( x = 0 \) into the equation: \[ y = \frac{2}{3}(0) + 3 = 0 + 3 = 3 \]
- The point (0, 3) satisfies the equation.
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For the point (5, 1):
- Substitute \( x = 5 \) into the equation: \[ y = \frac{2}{3}(5) + 3 = \frac{10}{3} + 3 = \frac{10}{3} + \frac{9}{3} = \frac{19}{3} \]
- Since \( \frac{19}{3} \) is approximately 6.33, it does not equal 1. Thus, the point (5, 1) does not satisfy the equation.
Based on this analysis, we conclude that the point (0, 3) is on the graph of the function \( y = \frac{2}{3}x + 3 \), while the point (5, 1) is not. Therefore, the given graph is not the graph of the function for both points.