Identify linear functions

Learning Objectives Define a linear function and its key characteristics. Identify a linear function from an equation by analyzing its form and the exponent of the variable. Determine if a table of values represents a linear function by calculating the rate of change. Recognize a linear function from its graph. Distinguish between linear and non-linear functions (e.g., quadratic) in various representations. Determine if a real-world scenario describes a linear relationship. Ever noticed how your total cost for streaming movies increases by the exact same amount for each movie you rent? 🎬 That's a linear function in action! This tutorial will teach you how to spot linear functions, which are a fundamental building block of algebra. You will learn to identify them from...

TermDefinitionExample FunctionA mathematical relationship where each input value (x) is paired with exactly one output value (y).In the function y = 2x, if the input is x=3, the only possible output is y=6. Linear FunctionA function whose graph is a single, non-vertical straight line. It has a constant rate of change.y = 3x + 2 is a linear function. For every 1 unit increase in x, y increases by a constant 3 units. Rate of Change (Slope)A ratio that describes how much the dependent variable (y) changes for every one unit of change in the independent variable (x). In a linear function, this value is constant.If a taxi costs $2.50 per mile, the rate of change is 2.50. The total cost increases by $2.50 for every mile driven. Degree of an EquationThe highest exponent of a variable in a single...

Slope-Intercept Form y = mx + b This is the standard form of a linear equation. If an equation can be rearranged into this form, it is linear. 'm' represents the constant rate of change (slope) and 'b' represents the initial value (y-intercept). Constant Rate of Change Formula m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} Use this formula to check if a table of values represents a linear function. Calculate the rate of change between several pairs of points. If the result is the same for all pairs, the function is linear. Linear Equation Checklist 1. The variable x has an exponent of 1 (or 0). 2. The variable x is not in the denominator. 3. The variable x is not under a radical sign (like a square root). Use this mental checklist t...