To find the equation of the line in point-slope form that goes through the point (7, 4) and is parallel to the line given by the equation \(3x - y = -2\), we first need to determine the slope of the given line.
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Convert the line to slope-intercept form (y = mx + b): \[ 3x - y = -2 \] Rearranging this equation, we get: \[ -y = -3x - 2 \] Multiplying by -1, we obtain: \[ y = 3x + 2 \]
From this, we see that the slope (\(m\)) of the line is 3.
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Since parallel lines have the same slope, the slope of our new line will also be 3.
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Using 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 through which the line passes. Plugging in \(m = 3\) and the point \((7, 4)\) into the equation, we have: \[ y - 4 = 3(x - 7) \]
Therefore, the equation of the line in point-slope form is: \[ y - 4 = 3(x - 7) \]