We plot the three points:

  

So we'll pick two of them and get the equation
of the line through them, and check to see if the
third point satisfies the equation.

We find the slope of the line through 
(5,19) (2,10) using the slope formula:

m = 
m = 
m = 
m = 3

Then we use the point-slope formula:

y - y1 = m(x - x1
y - 19 = 3(x - 5)
y - 19 = 3x - 15
     y = 3x + 4

Now we check to make sure the third given
point (-3,-5) satisfies that equation

     y = 3x + 4
    -5 = 3(-3) + 4
    -5 = -9 + 5
    -5 = -5

It does, so y = 3x + 4 is the function.

But we write it in function notation
by substituting f(x) for y:

    f(x) = 3x + 4

Edwin