To write the equation of a line that is parallel to the line given by the equation \(5x - y = 8\) and passes through the point \((7, 5)\), we need to first determine the slope of the given line.
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Convert the given line to slope-intercept form (y = mx + b): \[ 5x - y = 8 \] Rearranging gives: \[ -y = -5x + 8 \ y = 5x - 8 \] From this, we see that the slope \(m\) of the line is \(5\).
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Since parallel lines have the same slope, the line we want to find will also have a slope of \(5\).
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Use the point-slope form of the equation for the line: The point-slope form is given by: \[ y - y_1 = m(x - x_1) \] where \((x_1, y_1)\) is the point the line passes through, and \(m\) is the slope.
We plug in the point \((7, 5)\) and the slope \(5\): \[ y - 5 = 5(x - 7) \]
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Simplify this equation: \[ y - 5 = 5x - 35 \ y = 5x - 30 \]
Thus, the equation of the line that is parallel to \(5x - y = 8\) and passes through the point \((7, 5)\) is: \[ \boxed{y = 5x - 30} \]
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