Find the slope and the​ y-intercept for the line that passes through(2,2) and(7,7).

Find the slope first   =  rise / run  =  (y2-y1)/(x2-x1)        It does not matter which point you ascribe to '1' or '2'

m=slope = (7-2)/(7-2) = 5/5 = 1 

so y = mx + b   becomes   y= x + b    (m= slope = 1)

Plug one of your points into the equation to find 'b'

7 = 7 + b      so b = 0

your y =mx+b equation of a line becomes  y= x    because m= 1  and b= 0

y=mx+b =

y=(1)x + 0