Xy
-2 5
-1 3
0 1
1 -1
2 -3

find the explicit formula and the type of function

Just by looking at it, we can see that y decreases by 2 for every x value, so it's 
a (a can be any real number)-2x (it's -2 multiplied by x because it decreases by 2). Plugging it in for 0, we get a-2*0=1, and a=1, making the explicit function 
y=-2x+1. Since a linear equation is in the form y=mx+b (with m and b both representing any number), this fits the description.