To find the equation of the line that passes through the points (8, 4) and (11, 10), you can follow these steps:
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Calculate the slope (m) of the line using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \((x_1, y_1) = (8, 4)\) and \((x_2, y_2) = (11, 10)\): \[ m = \frac{10 - 4}{11 - 8} = \frac{6}{3} = 2 \]
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Use the point-slope form of the line equation, which is: \[ y - y_1 = m(x - x_1) \] Using point \((8, 4)\) and the slope \(m = 2\): \[ y - 4 = 2(x - 8) \]
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Simplify this equation: \[ y - 4 = 2x - 16 \] \[ y = 2x - 12 \]
Therefore, the equation of the line that passes through the points (8, 4) and (11, 10) is: \[ y = 2x - 12 \]