To determine which equation represents the graph based on the points (0, 3) and (-1, 4), we can follow these steps:
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Identify the points:
- The first point (0, 3) indicates that when \(x = 0\), \(y = 3\). This tells us that the y-intercept of the line is 3.
- The second point (-1, 4) tells us that when \(x = -1\), \(y = 4\).
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Calculate the slope (m) between the two points using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \((x_1, y_1) = (0, 3)\) and \((x_2, y_2) = (-1, 4)\): \[ m = \frac{4 - 3}{-1 - 0} = \frac{1}{-1} = -1 \]
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Write the equation in slope-intercept form (y = mx + b). We already found \(b = 3\) (y-intercept), and the slope \(m = -1\): \[ y = -1x + 3 \] or \[ y = -x + 3 \]
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Check against the provided options:
- A. \(y = -\frac{4}{5}x + 3\)
- B. \(y = \frac{5}{4}x + 3\)
- C. \(y = 3x + 5\)
- D. \(y = \frac{1}{2}x - 1\)
None of the provided options matches \(y = -x + 3\). Therefore, it appears none of the given options accurately represent the points (0, 3) and (-1, 4).
Conclusion: The correct slope-intercept equation for the given points is \(y = -x + 3\). If those four equations are the only possible answers, none of them is correct based on our calculations.