The points (2,-2) and(-4,13) lie on the graph of linear. funciton of x

Nice description.  But you've omitted or overlooked the instructions.  I'm assuming that you want to find the equation of this linear function.

                                              13-(-2)          15        -5
The slope of this line is m = = =  
                                               -4 -2             -6         2

Use the point-slope form of the equation of a straight line:

y-(-2) = (-5/2)(x-2), or y = -2 - (5/2)x + 5,   or  y = (-5/2)x + 3.