To determine if the graph of the line given by the equation \( y = -13x + 4 \) is correct based on the plotted points \( (0, 3) \) and \( (3, 2) \), we need to analyze the equation and its intercepts.
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Y-intercept: For the equation \( y = -13x + 4 \), the y-intercept (where \( x = 0 \)) is at \( y = 4 \). Thus, the y-intercept is \( (0, 4) \).
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Slope: The slope of the line from the equation \( y = -13x + 4 \) is -13, which indicates that the line has a negative slope.
Now examining the plotted points:
- The point \( (0, 3) \) is given, but it does not match the y-intercept we calculated (which is \( (0, 4) \)).
- The slope calculated using the two points \( (0, 3) \) and \( (3, 2) \) is positive. Specifically, the change in \( y \) per change in \( x \) would be \( \Delta y = 2 - 3 = -1 \) and \( \Delta x = 3 - 0 = 3 \), giving a slope of \( -\frac{1}{3} \).
From this analysis, the correct answer based on the information about the plotted points and the graph of \( y = -13x + 4 \) is:
No, it is not the correct graph because this graph used (0,3) as the y-intercept.