Math 1 · Unit 3 · Lesson 5
Linear Functions in the Real World
In a story, b is the starting amount or the flat fee, and m is the rate: the per hour, per month, per mile. Write the equation from the description and use it. Decide whether a situation is linear by checking for a constant rate of change. Then compare two linear functions given in different ways: which starts higher, which grows faster, when are they equal.
The big idea
A linear story has a start and a rate, and they are b and m. The starting amount, the flat fee, the height at the beginning: that is b, the value when x is 0. The per hour, per month, per mile: that is m, the slope, negative when the amount is going down. Write the model as rate times x plus start, then use it to predict, or set it equal to a target and solve. A situation is linear only when the rate is constant: the same change every step, which shows up as the same difference down a table. When two linear functions arrive in different clothes, an equation, a graph, a table, a story, pull m and b out of each and ask the same three questions: which starts higher, which grows faster, and when are they equal.
The parts of this lesson
Each part is its own short page. Go in order, or pick the one you need.
Printables
One page with start and rate, the linear test, the three comparison questions, and a worked comparison. Plus a worksheet with an answer key and a short lesson plan.