What you’ll learn
Interpret initial value.
Key idea
In a linear function the constant term is the input-zero output; the variable coefficient is the rate.
Initial value is output at zero; rate and first positive-input output are different quantities.
Worked example
Classify examples and non-examples for the concept 'Interpret initial value'.
For y=-5x+7, classify the initial value with zero-input evidence.
- Substitute x=0 in y=-5x+7; the variable term vanishes and y=7.
- The table row (0,7) gives initial output 7; constant per-unit difference -5 is the rate, a different quantity.
Answer: 7 is the initial value — x=0 gives y=7, while rate is -5.
Quick Check
Classify examples and non-examples for the concept 'Interpret initial value'.
For y=-3x-5, classify the initial value with zero-input evidence.