Complete a table for a two-variable relationship

Learning Objectives Identify input and output variables in a given relationship. Understand and interpret a given rule (equation) that relates two variables. Substitute numerical values into a rule to find corresponding output values. Accurately complete a table for a two-variable relationship when given a rule. Describe the relationship between two variables shown in a completed table. Extend a pattern in a two-variable table by applying the established rule. Ever wonder how stores figure out how much to charge for multiple items, or how many minutes you've talked on the phone? 📱💰 In this lesson, you'll learn how to fill in tables that show how two different things change together, using a simple rule. This skill helps us see patterns, organize information, and...

TermDefinitionExample VariableA letter or symbol (like 'x' or 'y') that represents a quantity that can change or take on different values.In the rule 'y = x + 5', 'x' and 'y' are variables. Two-Variable RelationshipA connection between two quantities where the value of one variable depends on the value of the other variable.The total cost of apples depends on the number of apples you buy. Rule (or Equation)A mathematical statement that describes exactly how two variables are related to each other.The rule 'y = 2x' means that 'y' is always twice 'x'. InputThe value that you start with and substitute into a rule or equation (often represented by the first variable, like 'x').If the rule is 'y = x...

Applying the Relationship Rule $$ \text{Output} = \text{Rule}(\text{Input}) $$ To find the output value for a given input, substitute the input value into the provided rule (equation) and perform the necessary calculations. Completing a Table Systematically $$ \text{For each Input value, calculate its corresponding Output value using the given Rule.} $$ Work through each row or column of the table one by one. Take each input value, apply the rule to it, and write the resulting output value in the correct place in the table. Identifying the Relationship Rule (Basic) $$ \text{Look for a consistent pattern: Output - Input = Constant} \text{ or } \text{Output / Input = Constant} $$ When given a partially filled table, observe how the output values relate to the input val...