for the equation y = 2x + 3, the equation is already in slope intercept form. (y = mx + b where m is the slope and b is the y intercept) so we know that the slope of that line is 2. two lines that are parallel have the same slopetwo lines that are perpendicular have slopes that are negative reciprocals of each other. Since the we want a line perpendicular to one with a slope of 2, we want the new line to have a slope of 1/2 so the new line would be y = 1/2x + b to solve for the correct b, you plug in the x and y point that the line is supposed to pass through, (3, 4)so 4 = 1/2(3) + b 4 = 3/2 + b 11/2 = b so your new line in slope intercept form is y = 1/2x + 11/2
