7D Variables & Patterns Study Guide

Key Vocabulary

Independent Variable — the variable you choose or control (input, usually x). (variable independiente)

Dependent Variable — the variable that changes based on the independent variable (output, usually y). (variable dependiente)

Input — the number you put INTO a rule or function. (entrada)

Output — the number that comes OUT after applying the rule. (salida)

Function Table — a table that shows the input-output pairs for a rule. (tabla de funciones)

Pattern — a repeated design or sequence that follows a rule. (patrón)

Rule: y = 3x + 1

Notice the pattern: each output goes up by 3.

1 Identify the input and output — What values are given? What are you finding?
2 Find the rule — Ask: "What do I do to the input to get the output?" Try adding, subtracting, multiplying, or dividing.
3 Test the rule — Make sure it works for ALL input-output pairs in the table.
4 Extend the pattern — Use the rule to find missing values.
5 Write the equation — Express the rule using variables (y = ...).

output = rule × input

y = mx + b

m = how much the output changes each time | b = the starting value

Independent variable (x) is what YOU choose. Dependent variable (y) depends on your choice.
The rule must work for ALL rows in the table, not just one.
Patterns can involve two operations. If multiplying alone doesn't work, try adding or subtracting too (e.g., y = 2x + 3).
Input goes first in an ordered pair: (input, output) = (x, y).

1. Use the rule y = 5x. What is y when x = 7?

2. Look at this table:

What is y when x = 4?

3. A gym charges $10 per month plus a $25 sign-up fee. The rule is y = 10x + 25. How much do you pay for 6 months?

4. In the equation y = 4x, which variable is the independent variable? Type "x" or "y".