To find the equation of the line that passes through the points \((4, -1)\) and \((2, -5)\), we can follow these steps:
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Calculate the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \((x_1, y_1) = (4, -1)\) and \((x_2, y_2) = (2, -5)\).
Substituting in the values: \[ m = \frac{-5 - (-1)}{2 - 4} = \frac{-5 + 1}{2 - 4} = \frac{-4}{-2} = 2 \]
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Use the point-slope form of the equation: The point-slope form of a line is given by: \[ y - y_1 = m(x - x_1) \] We can use point \((4, -1)\) and the slope \(m = 2\): \[ y - (-1) = 2(x - 4) \] Simplifying this: \[ y + 1 = 2(x - 4) \] \[ y + 1 = 2x - 8 \] \[ y = 2x - 8 - 1 \] \[ y = 2x - 9 \]
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Final Equation: The equation of the line in slope-intercept form is: \[ y = 2x - 9 \]