To determine which of the provided points is NOT a solution of the equation represented by the graph, we need to find the equation of the line that passes through the points \((-3.8, 0)\) and \((0, -4)\).
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Find the slope of the line: The slope \(m\) is given by the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points \((-3.8, 0)\) as \((x_1, y_1)\) and \((0, -4)\) as \((x_2, y_2)\): \[ m = \frac{-4 - 0}{0 - (-3.8)} = \frac{-4}{3.8} = -\frac{40}{38} = -\frac{20}{19} \]
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Use point-slope form of the line: The point-slope form of a line is: \[ y - y_1 = m(x - x_1) \] Using point \((0, -4)\): \[ y - (-4) = -\frac{20}{19}(x - 0) \] Simplifying this: \[ y + 4 = -\frac{20}{19}x \] \[ y = -\frac{20}{19}x - 4 \]
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Test the points to see if they are solutions of the line's equation \(y = -\frac{20}{19}x - 4\).
- For (2, -7): \[ y = -\frac{20}{19}(2) - 4 = -\frac{40}{19} - 4 = -\frac{40}{19} - \frac{76}{19} = -\frac{116}{19} \approx -6.1 \quad \text{(not -7)} \]
- For (-5, 4): \[ y = -\frac{20}{19}(-5) - 4 = \frac{100}{19} - 4 = \frac{100}{19} - \frac{76}{19} = \frac{24}{19} \approx 1.26 \quad \text{(not 4)} \]
- For (0, -4): \[ y = -\frac{20}{19}(0) - 4 = -4 \quad \text{(valid)} \]
- For (-2, -1): \[ y = -\frac{20}{19}(-2) - 4 = \frac{40}{19} - 4 = \frac{40}{19} - \frac{76}{19} = -\frac{36}{19} \approx -1.89 \quad \text{(not -1)} \]
Based on the calculations:
- \( (2, -7) \) does not satisfy the equation.
- \( (-5, 4) \) does not satisfy the equation.
- \( (0, -4) \) satisfies the equation.
- \( (-2, -1) \) does not satisfy the equation.
Now, to answer the question: the points that are NOT solutions are \( (2, -7) \), \( (-5, 4) \), and \( (-2, -1) \). Since the problem asks for one, we can say (2, -7) or (-5, 4).
Since we need to choose only one:
The final answer is (2, -7).