To determine whether the line joining the points (0, 3) and (3, 2) is the correct graph of the equation \( y = -13x + 4 \), we need to analyze both the line characteristics and the equation.
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Finding the slope: The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] For the points \((0, 3)\) and \((3, 2)\): \[ m = \frac{2 - 3}{3 - 0} = \frac{-1}{3} \] This indicates a negative slope, which contradicts the \( -13x + 4 \) equation as that would imply a much steeper negative slope (not -1/3).
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Finding the y-intercept: The y-intercept from the given points is (0, 3), indicating that when \( x = 0 \), \( y = 3 \). The y-intercept of the equation \( y = -13x + 4 \) is found by setting \( x = 0 \): \[ y = -13(0) + 4 = 4 \] This means the y-intercept of the line described by \( y = -13x + 4 \) is (0, 4).
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Conclusion: The graph that connects points (0, 3) and (3, 2) does not correspond to the equation \( y = -13x + 4 \) due to the slope and because it has a different y-intercept.
Therefore, the correct response is: No, it is not the correct graph because this graph used (0, 3) as the y-intercept.