Complete a table for a linear function

Learning Objectives Identify the components of a linear function rule. Substitute given input values into a linear function rule. Calculate corresponding output values accurately using the function rule. Organize input and output values into a complete table of values. Recognize the constant rate of change within a linear function's table. Verify the linearity of a function from its table of values. Ever wondered how a recipe tells you exactly how much sugar to add for a certain number of cookies? 🍪 That's a function at work, showing how one quantity depends on another! In this lesson, you'll learn how to complete tables for linear functions. These tables are like mathematical recipes that show how one quantity changes predictably with another, helping us se...

TermDefinitionExample Linear FunctionA relationship between two variables where the graph is a straight line, and the output changes by a constant amount for each unit change in the input.The equation `y = 2x + 3` represents a linear function. Function RuleAn equation that describes the specific mathematical operation(s) to be performed on the input to get the output.For `y = 2x + 3`, the rule is 'multiply the input by 2, then add 3'. Input (Independent Variable)The value that is put into a function; its value can be chosen freely and it affects the output. Often represented by `x`.In `y = 2x + 3`, if we choose `x = 5`, then 5 is the input. Output (Dependent Variable)The value that results from applying the function rule to the input; its value depends directly on the input. Oft...

General Form of a Linear Function `y = mx + b` This is the standard form for a linear function. Here, `x` is the input, `y` is the output, `m` is the slope (constant rate of change), and `b` is the y-intercept (the output when `x=0`). Substitution Principle for Functions To find the output `y` for a given input `x`, replace every instance of `x` in the function rule with the specific input value, then simplify the resulting expression. This rule guides how to use the function rule to calculate output values. For example, if `y = 3x - 1` and `x = 4`, substitute `4` for `x` to get `y = 3(4) - 1`. Order of Operations (PEMDAS/BODMAS) When evaluating expressions, follow the order: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addi...