To determine if the graph correctly represents the equation \( y = -\frac{1}{3}x + 4 \), we need to analyze its y-intercept and slope.
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Y-intercept: The y-intercept of the equation \( y = -\frac{1}{3}x + 4 \) is the point where \( x = 0 \). Substituting \( x = 0 \):
\[ y = -\frac{1}{3}(0) + 4 = 4 \]
So, the y-intercept is \( (0, 4) \).
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Slope: The slope of the equation \( y = -\frac{1}{3}x + 4 \) is \( -\frac{1}{3} \), which is negative, meaning the line should decrease as it moves from left to right.
Now, comparing this information to the plotted points provided:
- The graph shows points \( (0, 3) \) and \( (3, 2) \).
For the point \( (0, 3) \):
- At \( x = 0 \), the graph shows \( y = 3 \), not \( y = 4 \). This is a discrepancy since the correct y-intercept should be \( (0, 4) \).
For the slope calculation:
- The slope from point \( (0, 3) \) to point \( (3, 2) \) is:
\[ \text{slope} = \frac{2 - 3}{3 - 0} = \frac{-1}{3} \]
This slope is negative, which is consistent with the expected behavior of the line.
Final Assessment:
- The correct y-intercept for the line \( y = -\frac{1}{3}x + 4 \) is \( (0, 4) \), but the graph shows the y-intercept as \( (0, 3) \), which is incorrect.
Correct Answer: No, it is not the correct graph because this graph used \( (0, 3) \) as the y-intercept.