To determine if the graph corresponds to the equation \( y = -\frac{1}{3}x + 4 \), we can analyze the equation and the provided points.
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Identify the Y-Intercept: The equation \( y = -\frac{1}{3}x + 4 \) has a y-intercept at \( (0, 4) \). This is the point where the graph crosses the y-axis.
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Check the Given Points:
- The point \( (0, 3) \) indicates that at \( x = 0 \), \( y = 3 \), which does not correspond to the y-intercept calculated from the equation.
- The point \( (3, 2) \) can also be checked against the equation by substituting \( x = 3 \): \[ y = -\frac{1}{3}(3) + 4 = -1 + 4 = 3 \] This means that when \( x = 3 \), \( y \) should be \( 3 \), not \( 2 \) as stated.
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Conclusion on Options:
- Since the graph indicates that the y-intercept is \( (0, 3) \) instead of \( (0, 4) \) and does not match the slope of the given equation \( -\frac{1}{3} \), which is negative, the graph does not accurately represent the equation.
Based on this analysis, the correct answer would be: C. No, it is not the correct graph because this graph used (0, 3) as the y-intercept.
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