What is the slope-intercept form of the function described by this table?
x. 1 2 3 4
y. 2 7 12 17

Y=  kx+b,    k-slope,    b-intercept
so
2=k*1+b
7=k*2+b
12=k*3+b
17=k*4+b

solve these two equation:
2=k*1+b
7=k*2+b
second minus first is 7-2=2k-k+b-b
5=k,
 so we know k=5
 put this in any equation 2=5*1+b 
b=2-5
b=-3

check this in
12=5*3-3 - right
17=5*4-3 - right

y=5x-3