Math 1 · Unit 3 · Lesson 3 · part 8 of 9
Looking ahead: other families
Lines are the first family you have met.
Looking ahead: other families
Lines are the first family you have met. They will not be the last. Later units bring other families, each with its own form and its own numbers that move the graph around.
The line family
y = mx + b
Form: y = mx + b. Parameters: m tilts, b slides. This unit.
The exponential family
y = a · bˣ
Curves that start slow and then shoot up (or fall off). Its numbers set the starting value and how fast it multiplies. A later unit.
The quadratic family
y = ax² + bx + c
U-shaped curves. Its numbers set how wide the U is, which way it opens, and where it sits. A later unit.
The question to keep asking from now on. What family is this, and what does each number do to the graph? You already know the answer for lines: m tilts, b slides. Every new family gets the same three questions.
How each family growsA line grows by adding: the same amount, m, every step, so a table shows a constant difference. An exponential grows by multiplying: the same factor every step, so a table shows a constant ratio. A quadratic bends: its rate of change itself changes, so it curves and turns around at one point. Lines add, exponentials multiply, quadratics bend, and every one of them is just its family with the numbers filled in.