Math 1 · Unit 3 · Lesson 3 · part 2 of 9
One form, one family
Every straight line can be written y = mx + b.
One form, one family
Every straight line can be written y = mx + b. Same form, every time. Only the numbers change. A group of graphs that share the same form and differ only in their numbers is called a family of graphs, also called a family of curves. So all straight lines are one family, and each line is one member of it, picked out by its own m and its own b.
The numbers that pick out a member have a name too: parameters. m and b are the two parameters of the line family. Give me an m and a b and you have named exactly one line.
The habit we are building. Name the family. Find its numbers. Know what each number does to the graph. Lines are the first and simplest family, which is why we learn the habit here.