Free Linear Functions Worksheet

There is no escaping linear functions at school, so use our worksheets for drawing straight line graphs to present the topic in a clear and engaging way. Our linear functions worksheets are designed to help students to understand all aspects of lines, gradients and graphs. Our clear and concise straight line graph worksheets will help your child or pupil get to grips with finding gradients and drawing line graphs.  All of our linear functions worksheets have answers, so you can see how well students are doing and pinpoint areas for revision. After using our drawing line graphs worksheets, students will be able to find the equation of the line in no time!

Lines and Gradients Worksheets

At Cazoom our linear functions worksheets break down the complex world of straight lines and gradients into manageable and understandable chunks. Our line graph worksheets present crucial information in a clear and concise way and help students improve at finding gradients and drawing straight line graphs.

The Importance of Linear Functions in Real Life

Whenever there is a rate of change, this can be represented in the form of a linear function.

Whenever there is a rate of change, this can be represented in the form of a linear function. A linear function maps the relationship between two variables, and there are many situations in everyday life that could be drawn as a straight line graph. Working out how many miles a car traveled on a tank of fuel can be expressed as a linear function, as can working out how many of the same item you can buy for $10. Although not many people draw a straight line graph when doing their weekly shop, when a shopper calculates how many packets of biscuits they can buy with their available funds, they are forming a linear function in their head.

Understanding Speed, Distance and Time

Linear functions are frequently used to represent a change in a speed proportional to distance and time.

These types of graphs help children understand the relationship between speed, distance and time, concepts which they will need to master in order to gain confidence in math and science. Linear functions worksheets reinforce all the material they are being taught in class and worded problems can help children understand all the real-life situations in which linear functions are used. Math worksheets are an excellent resource for children of all abilities to help improve their knowledge and grow their skills.

A linear function, in its most basic form, is a function that can be graphed as a straight line. According to math experts at Columbia University, they are easy to work with and can be applied in many ways. (1) They are generally used to show data and how it changes, such as showing how something increases or decreases with time.

Linear functions are equations that can be written in different forms or plotted on a graph, where they will appear as a straight line. However, they cannot be a vertical line. They can be a horizontal line, but it is more likely the linear function will appear as a slanted line on a graph.

  • How Do You Know if It’s a Linear Function?

    There are a few ways to determine if a function is a linear function. The most common way is to rearrange the formula to slope-intercept form. If it can be put into slope-intercept form, it is a linear function. 

  • What is the Formula for Linear Functions?

    Linear functions are written as f(x)=mx+b. The letters m and b stand for constants, and the f(x) and (x) are variables. In a linear function, m would be the slope of the line and b would be the y-intercept of the line on the graph.

  • What is an example of a Linear Function?

    An example of a linear function would be f(x)=2x+3. In this example, the slope would be 2 while the y-intercept would be 3

Graphing linear equations can be done doing two different methods.

    • How Do You Graph Linear Functions?

      One way to graph the linear function is to find the y-intercept, then use the slope to find another point on the graph and draw a line between them. Another is to solve the equation to find two different points on the graph, then plot them and draw a line between them.

    • How Do You Know Which Method to Use?

      Use the method based on the type of information provided. If the linear function is in slope-intercept form, find the y-intercept and the slope to graph the function. If the linear function isn’t in slope-intercept form or one point is already known, use the other method.

Graphing linear function worksheets have been designed to help students practice solving linear functions and learning how to graph them.

    • How Can Graphing Linear Function Worksheets Help?

      Functions worksheets allow students to learn more about the equations that can be linear functions, how to solve the equations, and how to graph linear functions.

    • What Worksheets are Available?

      There are functions worksheets available that review drawing linear functions, drawing slopes, finding slopes, slope-intercept form, and more.

If a graph or two points are given, it is possible to write out the linear function using information from the graph.

    • What are the Methods for Writing Linear Equations?

      There are a couple of methods for writing linear equations. The first method is to find one point, and the slope on a graph then put the information in an equation in slope-intercept form. Another is to use two points on the graph or points that are given to create the linear equation.

    • What Do You Need to Write Linear Equations?

      To write a linear equation, you need a graph, two points that can be plotted on a graph, or one point along with a slope.

Word problems that involve linear functions can be solved by looking for the right information, then plotting it on a graph or using the information to create the equation.

    • What Information Do You Look for in Word Problems?

      In a word problem, look for two points that can be plotted on a graph or determine the y-intercept and the slope. If possible, go ahead and plot these on the graph to make it easier to see the function.

    • How Do You Solve Word Problems?

      Solve word problems by finding the information needed then writing the equation. Plot the function if possible, to make sure the answer is correct.

Linear functions are considered easy to understand because they are just a straight line on a graph. Use the linear function worksheets available to learn how to write, solve, and plot linear functions to get a better understanding of how they work and be able to solve them easily in any format.


1. Columbia University