(2,3)and (4,9) what’s the rate of change. y-intercept- equation-

The straight line is given by the equation
y=kx+b
We substitute coordinates of points
3=2k+b (1)
9=4k+b (2)
We give a system of equations
Solution of this system
(1) 2k=3-b
k=(3-b)/2
(2) 9=2(3-b)+b
9=6-b
b=-3
k=3
y=3x-3

Two main equations: slope = change in y divided by change in x & y-y initial= slope (x- x initial)
change in y= 9-3 = 6        change in x = 4-2 = 2
your initial points are (2,3)
slope is the rate of change.
once you have it, just plug it into the second equation. You'll get your equation and your y-intercept

Jim has run 5/6 of a mile so far. i hope that answers your question! good luck : )