To find the equation of the line that passes through the point (6, 3) and is parallel to the line represented by the equation \( y = -23x + 12 \), we start by noting that parallel lines have the same slope.
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Identify the slope of the given line: The slope (m) of the line \( y = -23x + 12 \) is \(-23\).
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Use the point-slope form for the point (6, 3): We can use the point-slope form of the equation of a line, which is given by: \[ y - y_1 = m(x - x_1) \] where \((x_1, y_1)\) is the point on the line and \(m\) is the slope. Here, we have: \((x_1, y_1) = (6, 3)\) and \(m = -23\).
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Substitute the values into the point-slope equation: \[ y - 3 = -23(x - 6) \]
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Distribute the slope: \[ y - 3 = -23x + 138 \]
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Solve for y to put the equation into slope-intercept form: \[ y = -23x + 138 + 3 \] \[ y = -23x + 141 \]
Thus, the equation of the line in slope-intercept form is: \[ \boxed{y = -23x + 141} \]
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