# Linear and nonlinear word problems worksheet

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## Linear Functions Worksheets

Linear vs. Nonlinear Equations Foldables. Now with 3 options! GREAT for interactive notebooks! MathAlgebra. ActivitiesMinilessonsPrintables. Add to cart. Wish List. This is an inquiry based lesson where students work together to discover which equations are linear versus non-linear.

Students are given 6 equations where they graph and make a table. Afterwords, a list of linear and nonlinear equations are made, and a place to record their thoughts as well as thei. MinilessonsHomeworkScaffolded Notes. Linear and Nonlinear activities: card sort and poster give students an opportunity to identify and compare linear and nonlinear equations. Included are 20 equations cards 10 linear and 10 nonlinear that are used for both activities. Card sort directions and headers are included along with poster.

MathAlgebraGraphing.Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with 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. Lesson 2 Summary Linear expressions are sums of constants and products of constants and raised to a power of 0 or 1. Non-linear expressions are also sums of constants and products of constants and a raised to a power that is not 0 or 1. The equal sign divides the equation into two parts, the left side and the right side. The two sides are called expressions.

Linear expressions are expressions that are sums of constants and products of a constant and x. However, non-linear expressions will have a power of that is not equal to 1 or 0. Example 1: A linear expression in is an expression where each term is either a constant, an x or a product of a constant and x.

Linear equation word problem - Linear equations - Algebra I - Khan Academy

What are they? Why or why not? You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.Previously, I have gone over a few examples showing how to solve a system of linear equations using substitution and elimination methods.

It is considered a linear system because all the equations in the set are lines. In this lesson, we will only deal with the system of nonlinear equations with two equations in two unknowns, x and y.

This system has two equations of each kind: a linear and a non-linear. Start with the first equation since it is linear. You can solve for x or y. Substitute the value of y into the second equation, and then solve for x. In this problem, move everything to one side of the equation while keeping the opposite side equal to zero. After doing so, factor out the simple trinomial, and then set each factor equal to zero to solve for x.

After solving the equation, we arrived at two values of x.

### Systems of Non-Linear Equations

Substitute these numerical values to any of the two original equations. Answer: — 3, 4. Then we should be able to solve for x. Use these values of x to find the corresponding values of y.

Answer: 0, 3. Answer: — 3, 0. The final answers are the points 0, 3 and — 3, 0. These are the points of intersections of the given line and circle centered at the origin. This problem is very similar to problem 2. We have a line top equation that intersects a circle bottom equation at two points. Step 1 : Solve the top equation for y. Here is the solution:. Answer: — 3, 2.

Step 4 : Here is the graph of the line intersecting the circle at — 3, 2 and 2, — 3. Substitute the expression of y from the top equation to the y of the bottom equation. Apply the distributive property then move everything to the left. Factor out the trinomial then set each factor equal to zero to solve for x. Since we now have the values of xpick any of the original equations to solve for y. Answer: —1, 2.

Answer: — 2, 1.When it comes to using linear systems to solve word problems, the biggest problem is recognizing the important elements and setting up the equations. Once you do that, these linear systems are solvable just like other linear systems. The same rules apply. The best way to get a grip around these kinds of word problems is through practice, so we will solve a few examples here to get you accustomed to finding elements of linear systems inside of word problems.

Example 1 : A farmhouse shelters 16 animals. Some of them are chickens and the others are cows. Altogether these animals have 60 legs. How many chickens and how many cows are in the farmhouse? First, to make the calculations clearer, we will choose symbols to represent the number of cows and the number of chickens.

Let us say that the chickens will be represented with x and the cows with y. Now, this task gave us enough information to make two equations. The first one is that the sum of the number of chickens x and the number of cows y is 16, since there are only 16 animals in the farmhouse. The second piece of information we have is that the total number of legs in the farmhouse is Since we know that cows have four legs each and chickens have two legs each, we have enough information to make another equation.

Now we have a system of linear equations with two equations and two variables. The only thing left to do now is to solve the system. We will solve it here for you, but if you need to remind yourself how to do that step by step, read the article called Systems of linear equations. We can now see that there are two chickens and 14 cows in the farmhouse. The next example will be a bit harder. How many forks and spoons did they make? As we did in the first example, we will first designate symbols to available variables.

So, the number of forks made will be represented with x and the number of spoons with y. Again, we have enough information to make two equations. Now all we have to do is to solve this linear system to find how many spoons and how many forks did we make last month. We can see that last month the store made and sold 17 forks and five spoons.

Although they can seem complicated, mastery and understanding of linear systems and associated word problems will come with a bit of practice. With experience you will be able to recognize their elements and solve even complicated systems with ease. Feel free to use the math worksheets below to practice solving this type of linear systems.

Home Contact. Free Math Worksheets is a math related website that contains pre-algebra, algebra and geometry worksheets and tests. Now, professors and teacher can reduce cheating by selecting printable exams to the individual students. Contact Us. Free Math Worksheets Help teachers to make an exam and students to get math worksheets.

Linear systems — word problems When it comes to using linear systems to solve word problems, the biggest problem is recognizing the important elements and setting up the equations.

Basic Mathematical Operations Basic mathematical operations Addition and subtraction Multiplying Divisibility and factors Order of operations Greatest common factor Least common multiple Squares and square roots.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.

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Identify the function rule, complete tables, evaluate, graph, compare and transform linear functions are some topics dealt with here. Printing Help - Please do not print inverse functions worksheets directly from the browser.

Kindly download them and print. 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.

Is the Function Linear or Nonlinear? 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.

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Examine the input x and output y values of the table in these linear function worksheets. If the rate of change for y with respect to x remains constant, then the table represents a linear function. Substitute the x-values in the linear expression to find the y-values in each function table worksheet.

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The easy level deals with integers, while the moderate level focuses on fractions and decimals. 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.

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. 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. 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 printable worksheets.

Members have exclusive facilities to download an individual worksheet, or an entire level. Login Become a Member. 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.

Graph 8th grade students learn to distinguish between linear and nonlinear functions by observing the graphs. Is the Function Linear or Nonlinear Table Examine the input x and output y values of the table in these linear function worksheets.

Linear Function Level 1 Substitute the x-values in the linear expression to find the y-values in each function table worksheet. Easy: Moderate:. Linear Function Level 2 Completing the function table in this batch of pdf worksheets comes with a twist. 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.

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Graphing Linear Functions Worksheets Plotting coordinates and graphing functions are the two major learning outcomes of this section of graphing linear equations worksheet printables. Comparing Linear Functions Compare two functions presented as tables, graphs and equations in these printable worksheets.

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 printable worksheets.

### Linear Vs Nonlinear

What's New?Note that solving trig non-linear equations can be found here. Sometimes we need solve systems of non-linear equationssuch as those we see in conics. Here are some examples. Note that we could use factoring to solve the quadratics, but sometimes we will need to use the Quadratic Formula.

Then use the intersect feature on the calculator 2 nd trace, 5, enter, enter, enter to find the intersection. Use trace and arrow keys to get close to each intersection before using intersect.

We can see that there are 3 solutions. The difference of two numbers is 3and the sum of their cubes is Find the numbers. The two numbers are 4 and 7.

They work! She immediately decelerates, but the police car accelerates to catch up with her. Assume the two cars are going in the same direction in parallel paths. We need to find the intersection of the two functions, since that is when the distances are the same.

Remember that the graphs are not necessarily the paths of the cars, but rather a model of the how far they go given a certain time in seconds.

We could also solve the non-linear systems using a Graphing Calculatoras shown below. Lacy will have traveled about feet when the police car catches up to her. Learn these rules, and practice, practice, practice!

Skip to content.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 pre-algebra and algebra 1 courses grades 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 generator below. Each worksheet is randomly generated and thus unique. The answer key is automatically generated and is placed on the second page of the file.

You can generate the worksheets either in html or PDF format — both are easy to print.

## Linear Equations in the real world

To get the worksheet in html format, push the button " View in browser " or " Make html worksheet ". Sometimes the generated worksheet is not exactly what you want. Just try again! To get a different worksheet using the same options:. Worksheets for writing expressions with variables from verbal expressions.

New concepts are explained in simple language, and examples are easy to follow. Word problems relate algebra to familiar situations, helping students to understand abstract concepts. Students develop understanding by solving equations and inequalities intuitively before formal solutions are introduced. Students begin their study of algebra in Books using only integers. Books introduce rational numbers and expressions. Books extend coverage to the real number system. Basic instructions for the worksheets Each worksheet is randomly generated and thus unique.

To get a different worksheet using the same options: PDF format: come back to this page and push the button again. Html format: simply refresh the worksheet page in your browser window. Ready-made worksheets 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.

Linear Equations Worksheet Generator. Choose the types of equations generated for the worksheet.