Question

Determining Initial Value

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 the initial value for Relationship 2 if Relationship 1 and Relationship 2 each have the same input when their output value is 50.

Answer 1

Let each relationship be linear: y = mx + b.
Relationship 1: y = (3/2)x + 5. Set y = 50 and solve for x:
50 = (3/2)x + 5 → 45 = (3/2)x → x = 45 · (2/3) = 30.

Relationship 2: y = (5/6)x + b2. Use x = 30 and y = 50:
50 = (5/6)·30 + b2 → 50 = 25 + b2 → b2 = 25.

So the initial value for Relationship 2 is 25.