Write a linear function given the following information

F(2) = 5 and F(3) = -1

ax + c = y
2a + c = 5 so c = 5 - 2a
3a + c = -1 so c = -1 - 3a

5 - 2a = -1 - 3a
5 + a = -1
a = -6, c = 17

F(x) = -6x + 17 is the correct answer, not -7 as Steven said.

F(2) = 5 and F(3) = -1

gives you two points
(2,5) and (3,-1)

first, the slope
(y1-y2)/(x1-x2)

either point can be 1 or 2
(-1-5)/(3-2)
-6/1

-6

so you start with
y= -6x

now subtract the values of a point from their relative x and y variable
(y-5)= -6(x+2)
y-5= -6x-12

y= -6x-7