Identify Linear Functions
Related Topics:
More Lessons for Grade 8
Math Worksheets
Videos, worksheets, and solutions to help Grade 8 students learn how to identify linear functions.
How to identify Linear Functions?
The following diagrams show how to identify linear functions. Scroll down the page for more examples and solutions.
Algebra Worksheets
Practice your Algebra skills with the following worksheets.
Printable & Online Algebra Worksheets
1. From an Equation:
A linear function in one variable (usually x) can be written in the general form:
Slope-intercept form: f(x) = mx + b or y = mx + b
or
Standard form: Ax + By = C
where A, B, and C are constants, and A and B are not both zero.
Key things to look for in the equation:
The variable (x) has a power of 1. You won’t see terms like x², √x, 1/x, etc.
The variable is not inside any other functions like sine, cosine, logarithm, or exponential functions.
There are no terms where the variable is multiplied by itself.
2. From a Graph:
The graph of a linear function is always a straight line.
How to identify a linear function from a graph:
Check if the points form a straight line. If you plot points of the function, they should all lie on a single, non-curved line.
A vertical line (like x = -5) is a linear equation but not a linear function.
3. From a Table of Values:
A linear function has a constant rate of change. This means that for every equal change in the input (x-values), there is a corresponding equal change in the output (y or f(x)-values).
How to identify a linear function from a table:
Calculate the difference in y-values (Δy) for equal differences in x-values (Δx).
Find the ratio Δy/Δx (which is the slope).
If this ratio (the slope) is constant throughout the table, then the function is linear.
Identifying Linear Functions
This video looks at identifying linear functions by graphs, sets of points, and equations. It includes a number of examples.
Recognizing Linear Functions
Linear Functions
Three different ways to determine if a function is linear or non-linear
Try out our new and fun Fraction Concoction Game.
Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.