To determine whether the graph represents the equation \( y = -\frac{1}{3}x + 4 \), let's analyze the equation step by step.
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Identify the y-intercept: In the equation \( y = -\frac{1}{3}x + 4 \), the y-intercept occurs when \( x = 0 \). Plugging \( x = 0 \) into the equation gives: \[ y = -\frac{1}{3}(0) + 4 = 4. \] Therefore, the y-intercept of the line is \( (0, 4) \).
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Check the slope: The slope of the line is \( -\frac{1}{3} \), which is negative. This means that the line should slope downwards as \( x \) increases.
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Analyze the given points: The points given in the question are \( (0, 3) \) and \( (3, 2) \). The first point \( (0, 3) \) indicates the y-coordinate when \( x = 0 \), and according to our analysis, the correct y-intercept from the equation should be \( (0, 4) \).
Given all of this:
- The y-intercept provided in the graph is \( (0, 3) \) instead of \( (0, 4) \).
- The graph's slope also indicates that it does not match the expected behavior of the equation.
Based on this reasoning, the correct response would be:
No, it is not the correct graph because this graph used (0, 3) as the y-intercept.