There seems to be an error in one of the coords: I think (-4,-16) should be (7,-16), because the other points are collinear. There would be 2 negative 4 x-coords which would mean it was not a function, or the second coord would be the independent variable and the function would be non-linear.

If we assume that the coords in order from left to right are:

(-4,-5), (2,-11), (5,-14), (7,-16)

then, there is a constant gradient: (-11-(-5))/(2-(-4))=-6/6=-1=(-14-(-11))/(5-2)=(-16-(-14))/(7-5).

So the slope is -1 and the equation can be found by plugging in any point, so let’s choose (-4,5):

y-(-5)=-1(x-(-4))=-(x+4), y+5=-x-4, so y=-x-9 or x+y+9=0. We can also write the function as f(x)=-x-9.