Linear Functions & Equations Worksheets

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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:

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.
Y-intercept (𝑏): The y-intercept is the point where the line crosses the y-axis (𝑥 = 0).
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

Graphs of Functions & Equations
More Printable Worksheets

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