we want the line perpendicular to the line 2x + y = 7, that is the line y = -2x + 7. so the slope of this line is -2. If two lines are perpendicular, then their slopes are the negative inverse of each other, therefore the line we want to find has slope = 1/2

using m = 1/2, (x1,y1) = (4,4), we have by the point-slope form:

y - y1 = m(x - x1)

=> y - 4 = (1/2)(x - 4)

=> y = (1/2)x - 2 + 4

=> y = (1/2)x + 2 .........this is the line passing through (4,4) perpendicular to 2x + y = 7