Math 1 · Unit 3 · Lesson 5 · part 5 of 6
Compare two linear functions
Two linear functions can be handed to you in different clothes: one as an equation, one as a graph, one as...
Compare two linear functions
Two linear functions can be handed to you in different clothes: one as an equation, one as a graph, one as a table, one as a story. To compare them, get m and b out of each one, the way Lesson 4 taught. Then ask three questions: which starts higher (bigger b), which grows faster (bigger m), and when are they equal.
Plan A, as an equation
cost = 10x + 20 (x months).
b = 20, m = 10 per month.
Plan B, as a table
| months | 0 | 1 | 2 |
|---|---|---|---|
| cost | 50 | 55 | 60 |
b = 50, m = 5 per month.
Compare
B starts higher (50 beats 20). A grows faster (10 per month beats 5). They are equal when 10x + 20 = 5x + 50: add −5x and −20 to both sides, 5x = 30, x = 6 months. Before 6 months A is cheaper; after 6 months B is cheaper.