What you’ll learn
Write linear function from two points.
Key idea
The rate is output change divided by input change, not either observed total.
An observed total at nonzero time is not the zero-time fee; both points must hold.
Worked example
Enter the exact value or ordered values in the format requested below.
A rental charges a linear total y dollars for x hours; 4 hours cost $11, 8 hours cost $19. Write the full linear model.
- The observed rate is (19-11)/(8-4)=2 dollars/hour.
- Substitute the complete first point: 11=2(4)+b, giving b=3. Model y=2x+3 verifies both observations.
Answer: y=2x+3
Quick Check
Choose which candidate representation satisfies the requirements of 'Write linear function from two points' and justify the choice.
A rental charges a linear total y dollars for x hours; 1 hours cost $7, 2 hours cost $9. Choose a model with BOTH-point evidence.