Complete a table for a two-variable relationship

Learning Objectives Identify the input and output variables in a given two-variable relationship. Substitute numerical values for a variable into a given algebraic equation. Accurately calculate the corresponding output values using a given rule or equation. Organize pairs of input and output values into a structured table. Extend a table of values by applying the given rule to new input values. Explain how a table represents a two-variable relationship. Have you ever wondered how a recipe tells you exactly how much sugar to add for a certain number of cookies? 🍪 That's a two-variable relationship in action! In this lesson, you'll learn how to complete tables that show how two quantities are related by a specific rule or equation. This skill is super useful for u...

TermDefinitionExample VariableA symbol, usually a letter (like 'x' or 'y'), that represents a quantity that can change or vary.In the equation y = x + 3, 'x' and 'y' are variables. Two-Variable RelationshipA connection between two quantities where the value of one quantity depends on the value of the other.The relationship between the number of hours worked (x) and the money earned (y). Equation (or Rule)A mathematical statement that shows the relationship between two variables, often using an equals sign.y = 2x is an equation where 'y' is always twice 'x'. Input ValueThe value you start with, which is substituted into the equation. It's often represented by 'x' and is usually the independent variable.If y = x + 5,...

Substitution Principle $$ \text{To find the value of an expression or equation, replace each variable with its given numerical value.} $$ This rule is fundamental for calculating output values. Whenever you have an input value for 'x', you 'substitute' it into the equation to find 'y'. General Form of a Linear Relationship $$ y = ax + b $$ Many two-variable relationships in Grade 7 can be expressed in this form, where 'a' and 'b' are constant numbers. 'a' represents a multiplier, and 'b' represents a constant addition or subtraction. For example, in y = 3x + 2, a=3 and b=2. Completing a Table of Values $$ \text{For each given input value (x), apply the rule (equation) to calculate the corresponding o...