Linear Equations Worksheets - BYJU'S

Linear Equations Worksheets

A linear equation is defined as an equation written for two contrasting variables. This equation is a linear combination of these two variables. Any linear equation plotted on a graph inevitably creates a straight line. There can be linear equations using one variable or multiple variables. The formula for linear equations is case-by-case and depends on the number of variables used.  Students are asked to calculate parameters or coefficients in linear equation worksheets using a linear equation formula....Read MoreRead Less

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Benefits of Linear Equation Worksheets:

Look around you and there are linear equations everywhere in our daily life. Linear equation worksheets can be of assistance for students when they step out into the real world. Ways in which we use linear equations on a daily basis are:

Calculating rates

Linear equation worksheets can prepare students for real world applications by helping them learn how to use these equations to determine the ratios of exchange rates, literacy rates, rate of consumption of electricity in an individual’s house, heart beat rates, and much more.

Making predictions

Mathematical models can be used to represent real-world situations. These models, often in the form of linear equations, can be used for many important issues such as predicting population changes in the next ten years, the possibility of rainfall using humidity as a variable, or calculating the distance at which two trains may meet, utilizing the velocities of both the trains as variables, or determining marketing policy changes.

Learning how to plot graphs

Curve-fitting is an essential mathematical skill. In science, plotting graphs are necessary for almost every experiment. Additionally, graph-potting helps students realize the importance of the extrapolation of data. Online linear equations worksheets can also help students learn about how to use various software such as Origin and MS Excel to plot points on a curve and draw inferences from experiments.

Exposure to statistical data Students become aware of how to handle statistical data when a curve is straightened. Values can be entered into graph-plotting software and easily fitted without a student manually plotting points on graph paper. The resultant databases can be crucial in conducting surveys related to the number of people succumbing to diseases, the number of businesses that have fallen prey to the financial crisis, and other similar scenarios.

Choose Math Worksheets by Topic

Adding and Subtracting Decimal Worksheets Adding and Subtracting Fractions Worksheets Adding and Subtracting Integers Worksheets Addition and Subtraction Worksheets Addition Worksheets Algebra Worksheets Area and Perimeter Worksheets Coins Worksheets Comparing Fractions Worksheets Comparing Numbers Worksheets Convert Fractions to Decimals Worksheets Coordinate Geometry Worksheets Data Data Handling Worksheets Decimals Worksheets Dividing Decimals Worksheets Dividing Fractions Worksheets Division Worksheets Exponents Worksheets Fact Family Worksheets Factoring Worksheets Fractions and Percents Worksheets Fractions Worksheets Geometry Worksheets Graphing Worksheets Integers Worksheets Linear Equations Worksheets Measurement Worksheets Money Worksheets Multiplication Worksheets Multiplying Decimals Worksheets Multiplying Fractions Worksheets Number Worksheets Order of Operations Worksheets Percents Worksheets Place Value Math Worksheets Place Value Worksheets Pre Algebra Worksheets Probability Worksheets Ratio and Proportions Worksheets Rational and Irrational Numbers Worksheets Rounding Worksheets Scientific Notation Worksheets Solving Inequalities Worksheets Subtraction Worksheets Time Worksheets Word Problems Worksheets

Linear Equation Worksheets Explained:

There are different types of linear equations that a student may be asked to solve when using linear equation worksheets. 

Regular use of linear equation worksheets can help students practice simplifying fractions or decimals within a linear equation by multiplying both sides by the lowest common multiple (LCM) of the denominators. Worksheets also help students understand that variables of an equation must be gathered on one side, while constants are placed on the other end of the ‘=’ sign, and that they can either multiply or divide in order to transform the coefficients of variables to 1.

Linear equation examples include:

  1.      x – 5 = 2;

therefore, x = 7.

  1.      x + 16 = 24;

therefore, x = 8.

  1.    6x = 48;

therefore, x = 8.

  1.    x/12 = 80;

therefore, x = 960.

More complex equations include:

  1.  x – (4x + 3) + 5x + (-2x -5) – 3 = 7x + 2 (-x – 8) – 4

     and

  1. 7x – (-2x – 6 ) – 6( -4x + 7) – 9 = 6 + 3 (-x-11) – 5 (6 + 2x) + 12

Students are also asked to plot a graph after solving an equation when using linear equation worksheets. For example:

  1.  y = -5x – 3.

In this example, the slope of the graph is -5. We know the slope of the line is bent downwards because of the minus sign. The y-intercept in this equation is -3. Therefore, the line will pass through the negative y axis. The number of intervals should be marked on the x axis and the values on the y axis.

The graph plotted for this equation will not be linear. In order to fit the graph in a straight line, an optimal distance must be maintained from every plotted point and the line must be somewhere along the middle of this cluster of points.

Once the graph is plotted, students may be asked to write the linear equation for it. If there is a y-intercept, it must be entered into the equation as the value of c. The slope, or m, may be calculated by drawing a triangle using the straight line, thereby determining the optimum x and y intervals. Then, the slope is measured using the formula: m= (maximum value of y – minimum value of y) / (maximum value of x – minimum value of x ). Upon determining the slope, the values of m and c are written to create the equation for a straight line: y = mx + c.

Printable Linear Equation Worksheets

Printable linear equation worksheets can help students understand how to solve linear equations, plot graphs from a set of given values, fit the curve, and write an equation by calculating the slope and y intercept of the curve. They are available in easily downloadable HTML and PDF formats. Students can use linear equation worksheets to enhance their understanding of this important aspect of algebra.

Frequently Asked Questions

The linear equations worksheets deal all about the linear equation concept, their examples, and practice problems. Ax + By = C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x + 3y = 5. When an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful. The linear equations worksheets help in learning these concepts easily. 

A nonlinear equation is one in which the highest degree of any term is two or greater. Since equation 1 has the highest degree of 2, and equation 2 involves variables x and y, this is an example of a nonlinear equation. X square + 2x + 1 = 0, 3x + 4y = 5, etc.

A linear equation is another name for the equation of a straight line. Lines are perpendicular to one another if the sum of the slopes of two straight lines equals one. The slope of two straight lines is the same if they are parallel to one another.

If an equation is written in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables. Examples of two-variable linear equations are 10x + 4y = 3 and – x + 5y = 2.

In linear equations worksheets, there are different kinds of questions based on the topic, and solving by using different methods for a better understanding of the concept and stepwise solutions will help in the self-assessment of the student. The worksheet is timed so, it will also help in the learning of time management.