To determine if the given graph correctly represents the equation \( y = -13x + 4 \), we need to analyze the characteristics of the line.
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Slope Calculation: The slope \( m \) of the equation \( y = -13x + 4 \) is \(-13\), which is a negative slope. This means that as \( x \) increases, \( y \) should decrease.
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Y-intercept Calculation: The y-intercept occurs when \( x = 0 \). Substituting \( x = 0 \) into the equation gives: \[ y = -13(0) + 4 = 4. \] Therefore, the y-intercept is \( (0, 4) \).
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Plotted Points: The graph indicates two plotted points: \( (0, 3) \) and \( (3, 2) \). The first point, \( (0, 3) \), shows the y-intercept is at 3, not 4, which conflicts with the calculated y-intercept of the equation.
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Slope Between Points: The slope between the two points \( (0, 3) \) and \( (3, 2) \) can be calculated as: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 3}{3 - 0} = \frac{-1}{3}, \] which is positive, indicating the line would rise rather than fall, further confirming that this does not match the expected negative slope of \(-13\).
Based on this analysis, the correct response is:
No, it is not the correct graph because this graph used \( (0, 3) \) as the y-intercept.