Algebra 1 / Unit 5: Linear Functions
5.5 Linear Models
Notes
A linear model describes a quantity that changes by the same amount each step.
- Identify the rate (slope) and the starting value ($y$-intercept), then write $y = mx + b$.
- From two data points, find the slope first, then $b$.
- Use the model to predict, and check that your answer makes sense in context.
Practice
A plumber charges a $60 visit fee plus $45 per hour. Which models the cost $C$ for $h$ hours?
The rate is $45 per hour and the fixed fee is $60.
A candle is 12 inches tall and burns 0.5 inch per hour. When will it burn out?
$12 - 0.5h = 0$, so $h = 24$.
A phone has 80% battery at 1 p.m. and 50% at 4 p.m. If it drains steadily, what is the rate?
$\displaystyle \frac{50 - 80}{4 - 1} = -10$.
Ready for more? Take the Unit 5 test.