Find an equation of the line through \( (4,8) \) and parallel to \( y=3 x+6 \). \( y=\square \) (Type your answer in slope-intercept form.)

To find the equation of a line that is parallel to the line given by \( y = 3x + 6 \) and passes through the point \( (4, 8) \), we first note that parallel lines have the same slope. The slope of the line \( y = 3x + 6 \) is \( 3 \). Therefore, the slope of the line we want to find is also \( 3 \). 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 \( m \) is the slope and \( (x_1, y_1) \) is a point on the line. Here, \( m = 3 \) and \( (x_1, y_1) = (4, 8) \). Substituting these values into the point-slope form: \[ y - 8 = 3(x - 4) \] Now, we simplify this equation: \[ y - 8 = 3x - 12 \] Adding \( 8 \) to both sides gives: \[ y = 3x - 12 + 8 \] \[ y = 3x - 4 \] Thus, the equation of the line in slope-intercept form is: \[ y = 3x - 4 \] So the final answer is: \[ y = 3x - 4 \]