(5)
Since, the relationship is linear
so, we can use point slope form of line and find equation of line 
we can select any two points 
first point is (4,10)
so, x1=4 , y1=10
second point is (7,17.5)
so, x2=7 , y2=17.5
now, we can find slope 

now, we can plug values


now, we can use point slope form of line 

now, we can plug values

we get 

Initial amount:
It is the value of y when x=0
so, we can plug x=0 and find y 


So, initial amount is 0
Rate of change:
we know that rate of change is slope 
so, m=2.5
so, the rate of change is 2.5
(6)
Since, the relationship is linear
so, we can use point slope form of line and find equation of line 
we can select any two points 
first point is (2,29)
so, x1=2 , y1=29
second point is (5,41)
so, x2=5 , y2=41
now, we can find slope 

now, we can plug values


now, we can use point slope form of line 

now, we can plug values

we get 

Initial amount:
It is the value of y when x=0
so, we can plug x=0 and find y 


So, initial amount is 21
Rate of change:
we know that rate of change is slope 
so, m=4
so, the rate of change is 4