To find the equation of the line that passes through the points \((3, 10)\) and \((-2, -20)\), we can follow these steps:
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Calculate the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Assign \((x_1, y_1) = (3, 10)\) and \((x_2, y_2) = (-2, -20)\).
\[ m = \frac{-20 - 10}{-2 - 3} = \frac{-30}{-5} = 6 \]
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Use the point-slope form of the equation: The point-slope form is given by: \[ y - y_1 = m(x - x_1) \] Using point \((3, 10)\) and slope \(m = 6\): \[ y - 10 = 6(x - 3) \]
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Simplify the equation: \[ y - 10 = 6x - 18 \] \[ y = 6x - 8 \]
Thus, the equation of the line that passes through the points \((3, 10)\) and \((-2, -20)\) is \[ \boxed{y = 6x - 8} \]