F(−4) = −5, f(1) = 4 (a) write the linear function f such that it has the indicated function values.

In this item, we may generate the coordinates of the point to which the points of the given function lie. 

For F(-4) = -5, the value of x = -4 and y = -5. Therefore, the coordinates of the point are (-4, -5)

For F(1) = 4, the value of x = 1 and y = 4. Hence, the coordinates of the point are (1, 4)

To generate the linear equation, we use the two-point formula:
    (y - y₁) = ((y₂ - y₁)/(x₂ - x₁))(x - x₁)

Substituting the known values,
   y - (-5) = ((4 - (-5)) / (1 - (-4))( x - (-4))

Simplifying,
   y  + 5 = 9x/5 + 36/5

Multiplying the equation by 5, 
      5y = 9x + 11

In standard form,
    9x - 5y = -11