Equations of Parallel Lines Write an equation in slope-intercept form for the line that passes through \( ( 3,2 ) \) and is parallel to \( y = 2 x + 1 \) .
The equation of the line in the slope-intercept form is \( y = 2 x + 1 \) . The slope of the parallel line is the same: \( m = 2 \) . So, the equation of the parallel line is \( y = 2 x + a \) . To find \( a \) , we use the fact that the line should pass through the given point: \( 2 = ( 2 ) \cdot ( 3 ) + a \) . Thus, \( a = - 4 \) . Therefore, the equation of the line is \( y = 2 x - 4 \) .