The parallel line to y = [tex]\frac{3}{2}[/tex] x + 3 and passes throughthe point (0 , 4) is y = [tex]\frac{3}{2}[/tex] x + 4Step-by-step explanation:Parallel lines have:1. The same slopes2. The different y-interceptThe slope-intercept form of the linear equation is y = m x + c, wherem is the slope of the line and c is the y-interceptWe need to find the equation of the line that is parallel to y = [tex]\frac{3}{2}[/tex] x + 3 and passes through the point (0 , 4)∵ The two lines are parallel∴ Their slopes are equal∵ The equation of the given line is y = [tex]\frac{3}{2}[/tex] x + 3∵ The form of the equation is y = m x + c∴ m = [tex]\frac{3}{2}[/tex]∴ The slope of the line is [tex]\frac{3}{2}[/tex]∵ The equation of the line is y = mx + c∵ m = [tex]\frac{3}{2}[/tex]∴ The equation of the line is y = [tex]\frac{3}{2}[/tex] x + c- To find c substitute x and y in the equation by the coordinates of a point lies on the line∵ The line passes through the point (0 , 4)∴ x = 0 , y = 4∴ 4 = [tex]\frac{3}{2}[/tex] (0) + c∴ c = 4∴ The equation of the line is y = [tex]\frac{3}{2}[/tex] x + 4The parallel line to y = [tex]\frac{3}{2}[/tex] x + 3 and passes throughthe point (0 , 4) is y = [tex]\frac{3}{2}[/tex] x + 4Learn more:You can learn more about equations of parallel lines in brainly.com/question/8628615#LearnwithBrainly