Linear Functions & Equations Worksheets

Printable “Function” worksheets:
What is a Function
Linear Function & Proportionality
Discrete & Non-Discrete Functions
Linear Functions & Equations
Word Problems & Linear Equations

Examples, solutions, videos, and worksheets to help Grade 7 and Grade 8 students learn examples of linear functions and how to describe a linear function using a linear equation.

Linear Functions & Equations

Linear Functions
A linear function is a function that represents a relationship between two variables where the rate of change is constant. The graph of a linear function is always a straight line.

General Form of a Linear Function:
𝑓(𝑥)= 𝑚𝑥 + 𝑏
Where:
𝑓(𝑥) is the output (dependent variable, often referred to as 𝑦),
𝑥 is the input (independent variable),
𝑚 is the slope of the line (which represents the rate of change),
𝑏 is the y-intercept (the value of 𝑓(𝑥) when 𝑥 = 0).

Key Characteristics of Linear Functions:

1. Constant Rate of Change (Slope 𝑚): The slope 𝑚 measures how much 𝑦 changes for a given change in 𝑥. If 𝑚 is positive, the function increases; if 𝑚 is negative, the function decreases.
   
2. Y-intercept (𝑏): The y-intercept is the point where the line crosses the y-axis (𝑥 = 0).
   
3. Graph: The graph of a linear function is always a straight line. Depending on the value of 𝑚, it can be upward sloping (positive slope), downward sloping (negative slope), or horizontal (zero slope).
   

Linear Equations
A linear function can be described using a linear equation, which represents a straight-line relationship between two variables. The equation that typically describes a linear function is written in the slope-intercept form:
𝑦 = 𝑚𝑥 + 𝑏
In this equation:
𝑦 is the output or dependent variable (the function value, often written as 𝑓(𝑥)),
𝑥 is the input or independent variable,
𝑚 is the slope of the line, which represents the constant rate of change,
𝑏 is the y-intercept, the point where the line crosses the y-axis (the value of 𝑦 when 𝑥 = 0).

Have a look at this video if you need to review discrete and non-discrete functions.

• Examples of Linear Functions & Equations

Click on the following worksheet to get a printable pdf document.
Scroll down the page for more Linear Functions & Equations Worksheets.

 

More Linear Functions & Equations Worksheets

Printable
(Answers on the second page.)
Linear Functions & Equations Worksheet #1
Linear Functions & Equations Worksheet #2
Linear Functions & Equations Worksheet #3
Linear Functions & Equations Worksheet #4

Related Lessons & Worksheets

Graphs of Functions & Equations
More Printable Worksheets

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.