The function of change of 3/2 whose graph passes through the point (4,10.5)

  f(x) = (3/2)x +9/2

Step-by-step explanation:

When you are given a point and a slope, the point-slope form of the equation of a line is useful. It can be written as ...

  y = m(x -h) +k

for a line with slope m through point (h, k).

Filling in your numbers gives ...

  y = (3/2)(x -4) +10.5

  y = (3/2)x -6 + 10.5 . . . . . use the distributive property

  y = (3/2)x + 9/2

Written in functional form, this is ...

  f(x) = (3/2)x + 9/2