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→ → Linear equations

Find here an unlimited supply of printable worksheets for solving linear equations, available as both PDF and html files. You can customize the worksheets to include one-step, two-step, or multi-step equations, variable on both sides, parenthesis, and more. The worksheets suit and courses (grades 6-9).

You can choose from SEVEN basic types of equations, ranging from simple to complex, explained below (such as one-step equations, variable on both sides, or having to use the distributive property). Customize the worksheets using the below.

Each worksheet is randomly generated and thus unique. The and is placed on the second page of the file.

You can generate the worksheets — both are easy to print. To get the PDF worksheet, simply push the button titled " " or " ". To get the worksheet in html format, push the button " " or " ". This has the advantage that you can save the worksheet directly from your browser (choose File → Save) and then in Word or other word processing program.

Sometimes the generated worksheet is not exactly what you want. Just try again! To get a different worksheet using the same options:

The simplest one-step equations, no negative numbers (grade 6).	One-step equations, no negative numbers, may need to simplify on one side first (grade 6).
One-step equations, the root may be negative (grade 7).	One-step equations, involving negative integers (grade 7).
Two-step equations (grades 7-8)	Two-step equations with negative integers (grades 7-8)
Equations including parentheses; use the distributive property (grades 7-8)	Variable on both sides and includes parentheses (grades 7-8)
Variable on both sides and includes parentheses & decimal numbers (grades 8-9)	Challenge: Equations with rational expressions (grades 8-9)

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Linear functions problems with solutions.

Linear functions are highly used throughout mathematics and are therefore important to understand. A set of problems involving linear functions , along with detailed solutions, are presented. The problems are designed with emphasis on the meaning of the slope and the y intercept.

Problem 1: f is a linear function. Values of x and f(x) are given in the table below; complete the table.

Problem 2: A family of linear functions is given by

Solution to Problem 2: a)

Problem 3: A high school had 1200 students enrolled in 2003 and 1500 students in 2006. If the student population P ; grows as a linear function of time t, where t is the number of years after 2003. a) How many students will be enrolled in the school in 2010? b) Find a linear function that relates the student population to the time t. Solution to Problem 3: a) The given information may be written as ordered pairs (t , P). The year 2003 correspond to t = 0 and the year 2006 corresponds to t = 3, hence the 2 ordered pairs (0, 1200) and (3, 1500) Since the population grows linearly with the time t, we use the two ordered pairs to find the slope m of the graph of P as follows m = (1500 - 1200) / (6 - 3) = 100 students / year The slope m = 100 means that the students population grows by 100 students every year. From 2003 to 2010 there are 7 years and the students population in 2010 will be P(2010) = P(2003) + 7 * 100 = 1200 + 700 = 1900 students. b) We know the slope and two points, we may use the point slope form to find an equation for the population P as a function of t as follows P - P1 = m (t - t1) P - 1200 = 100 (t - 0) P = 100 t + 1200

Problem 4: The graph shown below is that of the linear function that relates the value V (in $) of a car to its age t, where t is the number of years after 2000.

Problem 5: The cost of producing x tools by a company is given by

Problem 6: A 500-liter tank full of oil is being drained at the constant rate of 20 liters par minute. a) Write a linear function V for the number of liters in the tank after t minutes (assuming that the drainage started at t = 0). b) Find the V and the t intercepts and interpret them. e) How many liters are in the tank after 11 minutes and 45 seconds? Solution to Problem 6: After each minute the amount of oil in the tank deceases by 20 liters. After t minutes, the amount of oil in the tank decreases by 20*t liters. Hence if at the start there 500 liters, after t minute the amount V of oil left in the tank is given by V = 500 - 20 t b) To find the V intercept, set t = 0 in the equation V = 500 - 20 t. V = 500 liters : it is the amount of oil at the start of the drainage. To find the t intercept, set V = 0 in the equation V = 500 - 20 t and solve for t. 0 = 500 - 20 t t = 500 / 20 = 25 minutes : it is the total time it takes to drain the 500 liters of oil. c) Convert 11 minutes 45 seconds in decimal form. t = 11 minutes 45 seconds = 11.75 minutes Calculate V at t = 11.75 minutes. V(11.75) = 500 - 20*11.75 = 265 liters are in the tank after 11 minutes 45 seconds of drainage.

Problem 7: A 50-meter by 70-meter rectangular garden is surrounded by a walkway of constant width x meters.

Problem 8: A driver starts a journey with 25 gallons in the tank of his car. The car burns 5 gallons for every 100 miles. Assuming that the amount of gasoline in the tank decreases linearly, a) write a linear function that relates the number of gallons G left in the tank after a journey of x miles. b) What is the value and meaning of the slope of the graph of G? c) What is the value and meaning of the x intercept? Solution to Problem 8: a) If 5 gallons are burnt for 100 miles then (5 / 100) gallons are burnt for 1 mile. Hence for x miles, x * (5 / 100) gallons are burnt. G is then equal to the initial amount of gasoline decreased by the amount gasoline burnt by the car. Hence G = 25 - (5 / 100) x b) The slope of G is equal to 5 / 1000 and it represent the amount of gasoline burnt for a distance of 1 mile. c) To find the x intercept, we set G = 0 and solve for x. 25 - (5 / 100) x = 0 x = 500 miles : it is the distance x for which all 25 gallons of gasoline will be burnt.

Problem 9: A rectangular wire frame has one of its dimensions moving at the rate of 0.5 cm / second. Its width is constant and equal to 4 cm. If at t = 0 the length of the rectangle is 10 cm,

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></center></p><h2>Free Linear Functions Worksheet</h2><p>Math Worksheets / Algebra Worksheets / Free Linear Functions Worksheet</p><p>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!</p><h2>Lines and Gradients Worksheets</h2><p>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.</p><h2>The Importance of Linear Functions in Real Life</h2><p>Whenever there is a rate of change, this can be represented in the form of a linear function.</p><p>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.</p><h2>Understanding Speed, Distance and Time</h2><p>Linear functions are frequently used to represent a change in a speed proportional to distance and time.</p><p>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.</p><h2>What is a Linear Function?</h2><p>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.</p><h2>Understanding Linear Functions</h2><p>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.</p><h2>How Do You Know if It’s a Linear Function?</h2><p>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. </p><h2>What is the Formula for Linear Functions?</h2><p>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.</p><h2>What is an example of a Linear Function?</h2><p>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</p><h2>Graphing Linear Equations</h2><p>Graphing linear equations can be done doing two different methods.</p><h2>How Do You Graph Linear Functions?</h2><p>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.</p><h2>How Do You Know Which Method to Use?</h2><p>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.</p><h2>Graphing Linear Function Worksheets</h2><p>Graphing linear function worksheets have been designed to help students practice solving linear functions and learning how to graph them.</p><h2>How Can Graphing Linear Function Worksheets Help?</h2><p>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.</p><h2>What Worksheets are Available?</h2><p>There are functions worksheets available that review drawing linear functions, drawing slopes, finding slopes, slope-intercept form, and more.</p><h2>Writing Linear Equations</h2><p>If a graph or two points are given, it is possible to write out the linear function using information from the graph.</p><h2>What are the Methods for Writing Linear Equations?</h2><p>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.</p><h2>What Do You Need to Write Linear Equations?</h2><p>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.</p><h2>Word Problems for Linear Functions</h2><p>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.</p><h2>What Information Do You Look for in Word Problems?</h2><p>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.</p><h2>How Do You Solve Word Problems?</h2><p>Solve word problems by finding the information needed then writing the equation. Plot the function if possible, to make sure the answer is correct.</p><h2>Cazoom Maths Linear Function Worksheets Are Easy to Understand</h2><p>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.</p><p>1. Columbia University</p><p>http://www.columbia.edu/itc/sipa/math/linear.html</p><h2>GET 30 FREE MATH WORKSHEETS!</h2><p>Fill out the form below to get 30 FREE math worksheets.</p><p><center><img style=

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Linear Functions Worksheets

This collection of linear functions worksheets is a complete package and leaves no stone unturned. Eighth grade and high school students gain practice in identifying and distinguishing between a linear and a nonlinear function presented as equations, graphs and tables. Identify the function rule, complete tables, evaluate, graph, compare and transform linear functions are some topics dealt with here. Start off your functions practice with our free worksheets!

Identify Linear and Nonlinear Functions from Equation

Try this set of linear vs nonlinear functions worksheet pdfs to determine whether a function is linear or not. If the equation can be written in the slope-intercept form, y=mx+b then it is linear.

Download the set

Is the Function Linear or Nonlinear? | Graph

8th grade students learn to distinguish between linear and nonlinear functions by observing the graphs. The graph of a linear function is a straight line, while the graph of a nonlinear function is a curve.

Is the Function Linear or Nonlinear? | Table

Examine the input(x) and output(y) values of the table inthese linear function worksheets for grade 8. If the rate of change for y with respect to x remains constant, then the table represents a linear function.

Linear Function | Level 1

Substitute the x-values in the linear expression to find the y-values in each function table worksheet. The easy level deals with integers, while the moderate level focuses on fractions and decimals.

Linear Function | Level 2

Completing the function table in this batch of pdf worksheets comes with a twist. Students are expected to plug in either the input or output values in the function rule to determine the missing value.

Finding the Function Rule

Deciphering the pattern that converts the input into an output value in each table and writing it as an expression is all one is expected to do in this set of printable function rule worksheets for high school students.

Graphing Linear Functions Worksheets

Plotting coordinates and graphing functions are the two major learning outcomes of this section of graphing linear equations worksheet printables. The slopes here are expressed as integers and fractions.

(30 Worksheets)

Comparing Linear Functions

Compare two functions presented as tables, graphs and equations in these printable worksheets. Find the slope, x and y-intercepts to complete the table and answer questions based on comparisons.

Transformation of Linear Functions Worksheets

Draw a transformed graph, write a transformed function using horizontal and vertical shifts, stretches, compressions, and reflections too with these transformation of linear functions worksheets.

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Linear Equations Worksheets

Linear equations are equations that have two variables and are a straight line when graphed, based on their slope and y-intercept. Hence, linear equations worksheets have a variety of questions that help students practice key concepts and build a rock-solid foundation of the concepts.

Benefits of Linear Equations Worksheets

Linear equations worksheets are a great resource for students to practice a large variety of problems. These math worksheets are supported by visuals which help students get a crystal clear understanding of the topic. The variety of problems that these worksheets offer helps students approach these concepts in an engaging and fun manner.

Linear equations worksheets come with visual simulation for students to see the problems in action, an answer key that provides a detailed step-by-step solution for students to understand the process better, and a worksheet with detailed solutions.

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Students can practice problems by downloading the linear equations worksheets in PDF format for free.

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Linear Equations

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Linear Functions worksheets are an essential resource for teachers who want to provide their students with a comprehensive understanding of math concepts. These worksheets cover a wide range of topics, including slope-intercept form, point-slope form, and graphing linear equations. By incorporating these worksheets into their lesson plans, teachers can ensure that their students gain a solid foundation in linear functions, which is crucial for success in higher-level math courses. Additionally, these worksheets can be easily adapted to suit the needs of students at various grade levels, making them a versatile and valuable tool for educators.

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Worksheets for linear equations
You can customize the worksheets to include one-step, two-step, or multi-step equations, variable on both sides, parenthesis, and more. The worksheets suit pre-algebra and algebra 1 courses (grades 6-9). You can choose from SEVEN basic types of equations, ranging from simple to complex, explained below (such as one-step equations, variable on ...
Linear Equation Word Problems Worksheet
Free worksheet(pdf) and answer key on the solving word problems based on linear equations and real world linear models. Scaffolded questions that start relatively easy and end with some real challenges. Plus model problems explained step by step
Linear Functions Problems with Solutions
Problem 1: f is a linear function. Values of x and f (x) are given in the table below; complete the table. Solution to Problem 1: f is a linear function whose formula has the form. f (x) = a x + b. where a and b are constants to be found. Note that 2 ordered pairs (-3,17) and (4,-18) are given in the table.
Algebra 1 Worksheets
Graphing Absolute Values Worksheets. These Linear Equations Worksheets will produce problems for practicing graphing absolute values. These Linear Equations Worksheets are a good resource for students in the 5th Grade through the 8th Grade. These Algebra 1 generator allows you to produce unlimited numbers of dynamically created linear equations ...
PDF Worksheet
Review of Linear Functions (Lines) Find the slope of each line. Find the slope of the line through each pair of points. Find the slope of each line. Find the slope of a line parallel to each given line. Find the slope of a line perpendicular to each given line. Sketch the graph of each line. Write the slope-intercept form of the equation of ...
Linear equations, functions, & graphs
This topic covers: - Intercepts of linear equations/functions - Slope of linear equations/functions - Slope-intercept, point-slope, & standard forms - Graphing linear equations/functions - Writing linear equations/functions - Interpreting linear equations/functions - Linear equations/functions word problems
Linear equations & graphs
Let's explore different ways to find and visualize slopes and intercepts, and how these concepts can help us solve real-world problems. ... Linear equations word problems: graphs Get 3 of 4 questions to level up! Graphing linear relationships word problems Get 3 of 4 questions to level up!
Linear Functions Worksheets
Linear functions worksheets give students the opportunity to solve a wide variety of problems helping them to build a robust mathematical foundation. Linear functions worksheets help kids to improve their speed, accuracy, logical and reasoning skills in performing simple calculations related to the topic of linear functions.
Linear Equation Worksheets
Enjoy these free printable worksheets. Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key. Mixed Problems on Writing Equations of Lines Slope Intercept Form Worksheet Standard Form Worksheet Point Slope Worksheet
Linear Functions Worksheet (No. 1 Source)
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.
Algebra 2 Worksheets
These Algebra 2 Linear Equations Worksheets will produce problems for practicing graphing absolute values. These Linear Equations Worksheets are a good resource for students in the 8th Grade through the 12th Grade. These Algebra 2 generators allow you to produce unlimited numbers of dynamically created linear Linear functions worksheets.
Linear Function Worksheets
Start off your functions practice with our free worksheets! Identify Linear and Nonlinear Functions from Equation. Try this set of linear vs nonlinear functions worksheet pdfs to determine whether a function is linear or not. If the equation can be written in the slope-intercept form, y=mx+b then it is linear. Download the set.
Linear Equations Worksheets with Answer Key
Linear equations require students to work with a single variable of degree 1. So solving them are pretty simple and can be attempted by kids in grades 6-8. More Linear Equations Worksheets Graphing Linear Equations Worksheets Linear Equations Word Problems Worksheets Systems of Linear Equations worksheets Writing Equations of Lines Worksheets
Linear Equations Worksheets
Benefits of Linear Equations Worksheets. Linear equations worksheets are a great resource for students to practice a large variety of problems. These math worksheets are supported by visuals which help students get a crystal clear understanding of the topic. The variety of problems that these worksheets offer helps students approach these ...
Linear Equations (Worksheets)
On these printable worksheets, students will practice solving, finding x and y intercepts, and graphing linear equations. Solve to find the x- and y-intercepts. There are 6 problems to complete on this double-sided worksheet. Students will solve for the x- and y-intercepts and then use the slope formula to find the slope of the linear equations.
Linear equations and functions
Learn. Linear graphs word problems. Modeling with tables, equations, and graphs. Linear graphs word problem: cats. Linear equations word problems: volcano. Linear equations word problems: earnings. Modeling with linear equations: snow. Linear function example: spending money. Fitting a line to data.
PDF Simple Linear Equations (A)
Algebra Worksheet -- Solving Linear Equations (Including Negative Values) -- Form ax ± b = c Author: Math-Drills.Com -- Free Math Worksheets Subject: Mathematics Algebra Keywords: algebra, mathematics, math, solving linear equations Created Date: 8/24/2011 12:18:30 PM
50+ Linear Functions worksheets on Quizizz
These worksheets cover a wide range of topics, including slope-intercept form, point-slope form, and graphing linear equations. By incorporating these worksheets into their lesson plans, teachers can ensure that their students gain a solid foundation in linear functions, which is crucial for success in higher-level math courses.
Working with Linear Equations Worksheets
This Linear Functions Worksheet will produce problems for practicing solving the equation of a linear equation. This worksheet is a great resources for the 5th, 6th Grade, 7th Grade, and 8th Grade. Language for the Linear Functions Worksheet
PDF Linear Function Word Problems
Worksheet by Kuta Software LLC-2-4) An insurance company has an initial charge to insure jewelry, plus a charge per dollar value of ... Answers to Linear Function Word Problems 1) a. ind is number of people, dep is cost b. $7.75 per person c. $20 d. $151.75 e. 61 people 2) a. ind is time and dep is distance b. -93km/h c. 1019km d. 251.75km e. ...
Linear models word problems (practice)
Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. ... Linear equations word problems: earnings. Modeling with linear equations: snow. Linear equations ...
Systems of Linear Equations Worksheets and Answer Keys
Free worksheets(pdf) with answers keys on solving systems ofl inear equations. Each sheet starts out relatively easy and end with some real challenges. Plus model problems explained step by step
Full-Length SAT Suite Practice Tests
Find full-length practice tests on Bluebook™ as well as downloadable paper (nonadaptive) practice tests to help you prepare for the SAT, PSAT/NMSQT, PSAT 10, and PSAT 8/9.