Question

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.

Answer 1

Answer:

Sample Response: The equation of Relationship 1 is y = 3/2x + 5. Substitute 50 for y and solve to find that x = 30. Multiply 30 by 5/6, the rate of change of Relationship 2, to get 25. This means that the initial value would need to be 25 to get to 50 when the input is 30.

Answer 2

Answer:
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 $\frac{5}{6}$ and an initial value of c.
Therefore, the equation of Relationship 2 is:
y = $\frac{5}{6}$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 = $\frac{5}{6}$x + c
50 = $\frac{5}{6}$ * (30) + c
50 = 25 + c
c = 50 - 25
c = 25
This means that Relationship 2 has an initial value of 25

Hope this helps :)