The two coordinates allow us to work out the gradient and the intercept. Fortunately for us, coordinate A (0,3), gives us the y intercept, since the line intercepts the y axis when the x coordinate is zero - therefore our initial value is 3.
The gradient is how much y increases for each one x.
Therefore we work out the difference - between A and B, x increases by 2 and y increases by 4.
Dividing them, 4/2 gives us 2, i.e. y increases by 2 for each unit x.
We can write this as an equation:
[tex]\boxed{y=2x+3}[/tex]
Putting this together, the rate of change is 2 and the initial value is 3.
