Identify linear functions (Tutorial)

Learning Objectives Define a linear function and its key characteristics. Identify linear functions from equations by checking the form and variable exponents. Identify linear functions from a table of values by calculating the rate of change (first differences). Identify linear functions from a graph by observing its shape. Distinguish between linear and non-linear functions (e.g., quadratic) in various forms. Explain why a constant rate of change is the defining feature of a linear function. Ever notice how a phone bill with a flat fee plus a cost per gigabyte of data goes up by the same amount for each extra gigabyte you use? 📱 That's a linear function at work! In this tutorial, you will learn the three main ways to identify a linear function: from its equation, a...

TermDefinitionExample Linear FunctionA function that creates a straight line when graphed. Its key feature is a constant rate of change.y = 2x + 1 Rate of ChangeA ratio that describes how much the dependent variable (y) changes for every one-unit change in the independent variable (x). In a linear function, this is always constant.If you earn $15 per hour, the rate of change of your earnings is 15. Slope (m)The numerical value of a line's steepness and direction; it is the constant rate of change for a linear function.In the equation y = -3x + 5, the slope is -3. y-intercept (b)The point where the graph of a function crosses the vertical y-axis. It is the value of y when x is 0.In the equation y = 2x + 7, the y-intercept is 7, or the point (0, 7). First DifferencesThe differences bet...

Slope-Intercept Form y = mx + b This is the most direct way to identify a linear equation. If you can write an equation in this form, it's linear. 'm' is the slope and 'b' is the y-intercept. The exponents on x and y must be 1. Standard Form Ax + By = C Another common form of a linear equation, where A, B, and C are constants. As long as x and y are not multiplied together and their exponents are 1, an equation in this form is linear. Constant Rate of Change (Slope Formula) m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} Use this to test if a set of points from a table represents a linear function. Pick any two pairs of points; if the calculated slope 'm' is the same for all pairs, the function is linear.