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When x changes by  3, y changes by   (13 - a)

From  4 to 13   x changes by 9  so  y changes by  3 (13 - a)=   39 - 3a

And  notice that

39 - 3a =  b   rearrange   as

3a + b =  39 

The function, g or k ? is linear, so its graph will be a straight line, in which case the gradient between x = 1 and x = 4  will be the same  as that between x = 4 and x = 13.

So,

$\displaystyle \frac{b-13}{13-4}=\frac{13-a}{4-1}.$

From that,

$\displaystyle 3b-39=117-9a,\\ 9a+3b=156, \\ 3a + b = 52.$

Alternatively, let the equation of the function be $\displaystyle f(x) = Ax + B.$

Substituting the co-ordinates of the three points, we have

$\displaystyle a = A+B, \dots(1) \\13=4A+B, \dots(2) \\ b = 13A+B, \dots (3)$

from which,

$\displaystyle 3a+b = 3(A+B)+(13A+B)=16A+4B=4(4A+B)=52.$