Complete a table for a linear function

Learning Objectives Define key terms related to linear functions and tables of values. Identify the input (independent variable) and output (dependent variable) in a linear function. Substitute given input values into a linear function's equation. Accurately calculate the corresponding output values for a linear function. Complete a table of values for a given linear function. Recognize the relationship between a linear function's equation and its table of values. Ever wondered how a simple rule can create a whole list of related numbers? 🔢 Let's discover how to fill in the blanks! In this lesson, you'll learn how to complete tables for linear functions. This skill is fundamental for understanding how functions work, visualizing their behavior, and prep...

TermDefinitionExample Linear FunctionA function whose graph is a straight line. It can be written in the form \(y = mx + b\), where \(m\) and \(b\) are constants.The equation \(y = 2x + 1\) is a linear function. If \(x=3\), then \(y = 2(3) + 1 = 7\). Input (Independent Variable)The value that is put into a function. It is typically represented by the variable \(x\) and can be chosen freely.In the function \(y = 3x - 5\), the value of \(x\) is the input. If we choose \(x=4\), then 4 is the input. Output (Dependent Variable)The value that results from applying the function rule to an input. It is typically represented by the variable \(y\) and its value depends on the input.In the function \(y = 3x - 5\), the value of \(y\) is the output. If \(x=4\), then \(y = 3(4) - 5 = 12 - 5 = 7\), so 7...

General Form of a Linear Equation \(y = mx + b\) This is the standard form for a linear function, where \(x\) is the input, \(y\) is the output, \(m\) is the slope (rate of change), and \(b\) is the y-intercept (the output when \(x=0\)). Rule for Completing a Table For each given input value (\(x\)), substitute it into the function's equation and calculate the corresponding output value (\(y\)). This rule is applied sequentially for every empty row in the table. It ensures that each \(x, y\) pair satisfies the given linear function.