Relationship 1 has an initial value of 5 and a rate of change of 3/2. relationship 2 has a rate of change of 5/6. explain how to find what the initial value of relationship 2 needs to be for it to have an output of 50 with the exact same input as relationship 1.

initial value of Relationship 2 is 25

Explanation:
1- Considering Relationship 1:
It has initial value of 5 and rate of change of 1.5
Therefore, its equation would be:
y = 1.5x + 5
Now, we want the output to be 50. This means that:
50 = 1.5x + 5
50 - 5 = 1.5x 
45 = 1.5x
x = 30
Therefore, the output will be 50 when the input is 30.
The point is (30,50)

2- Considering Relationship 2:
It has a rate of change of  and an initial value of c.
Therefore, the equation of Relationship 2 is:
y = x + c
We have calculated that an output of 50 will occur at an input of 30 for Relationship 1. 
We are given that this scenario will also occur is Relationship 2.
Therefore, point (30,50) will satisfy Relationship 2.
We can now solve for c as follows:
y = x + c
50 = * (30) + c
50 = 25 + c
c = 50 - 25
c = 25
This means that Relationship 2 has an initial value of 25

Hope this helps :)