To determine whether the line connecting the points (0, 3) and (3, 2) corresponds to the equation \( y = -\frac{1}{3}x + 4 \), we need to analyze both the slope of the line formed by those points and the y-intercept.
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Calculate the Y-Intercept: The equation \( y = -\frac{1}{3}x + 4 \) has a y-intercept of (0, 4), as when \( x = 0 \), \( y \) equals 4.
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Check the Given Points: The points provided are (0, 3) and (3, 2). Here, at \( x = 0 \), the value of \( y \) is 3, which indicates that the y-intercept of this graph is (0, 3) rather than (0, 4).
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Calculate the Slope: The slope between the two points can be calculated as follows: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 3}{3 - 0} = \frac{-1}{3} \] Since the slope is negative, it matches the coefficient in the given equation.
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Conclusion: The correct y-intercept for the graph based on the provided points (0, 3) and (3, 2) is (0, 3), not (0, 4) as stated in the equation \( y = -\frac{1}{3}x + 4 \).
Therefore, the answer is:
No, it is not the correct graph because this graph used (0, 3) as the y-intercept.
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