Question 1157199
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Ok, linear means  f(x) = kx + c   where k and c are constants.  Notice how x is raised only to the first power, that's what makes it linear.


f(-2) = 3 tells us   k(-2) + c = 3
f(5) = 7  tells us   k(5) + c = 7
                     
  Subtract the bottom equation from the top, -7k = -4  --> k=4/7
  Plug in k=4/7 into one of the equations and solve for c:
      -2(4/7) + c = 3
        -8/7 + c = 3
          c = 3 + 8/7 = 21/7 + 8/7 = 29/7

{{{ highlight( f(x) = (4/7)x + 29/7 ) }}}