# Linear Equations – Examples, PDF

Lines are illustrations of the relationship between two points in a given plane. This means that the make and the direction are directly affected by the location of the two points. You can easily illustrate this relationship through linear equations and lines.

## What Are Linear Equations

Linear equations are equations that illustrate the proportional relationship between two variables and points. Simple linear equations are equations with a single variable, while there are linear equations with two variables, and even linear equations with three variables. All of which have their systems of linear equations and ways of solving said linear equations.

## How to Graph Linear Equations

A can come in many different forms. The standard form of a linear equation with two variables is Ax + By = C where x is the X coordinate, y is the Y coordinate, and C is the constant number. One variable linear equation will come in the form of Ax + B = C.

### 1.) Write Down the Equation

Begin by writing down the equation in a physical note, or digital note-taking software. This will help you visualize the equation without needing to backread the question.

### 2.) Discern Whether the Equation has One Point or Two Points

When you have finished writing down the equation, check whether the equation has one point or two points. You will be able to know this by the presence of X and Y coordinates in the equation. If the equation follows the Ax + By + C = 0 formats, it will require specific X and Y values that you can obtain from a different formula. Only use this how-to with equations that use the standard form of the linear equation or the standard one-variable linear equation.

### 3.) Simplify the Equation

When you have finished discerning the equation, you must simplify the equation to its simplest form. This means if there is a common denominator between the three variables, then you must divide them by said common denominator.

### 4.) Isolate One of the Points in the Equation

After you have simplified the equation, you must isolate and move one of the variables to the equals sign. The equation would either come in the form of x = C – B, Ax = C – By, or By = C – Ax.

### 5.) Equate the Isolated Point to a Specific Number, and Solve for the Second Point

After isolating one of the points, you must now substitute the isolated variable with specific points. For example, if 2x = 2 – Y is the linear equation, we can substitute the x value to be x = 0. The equation will then become 2(0) = 2 – Y, which will equal to Y = 2.

### 6.) Repeat Step Five at least Four Times, and Graph the Coordinates

Repeat these steps until you have up to four sets of X and Y coordinates, note that each set will be a pair. Following the example above, the set of X and Y coordinates will be (0,2). Once you have four sets of these coordinates, graph the linear equation into the cartesian plane using these coordinates as your reference points. Afterward, you will connect all the reference points to create a straight line.

## Why are linear equations very important?

Linear equations are equations that can describe how one variable affects another variable in a straight line, hence the word linear. This means that the effect is stable and works at a steady predictable rate, this is very important as there are effects that are unstable and unpredictable. Linear equations allow scientists, engineers, and everyday people to incorporate mental calculations on specific objects, events, and phenomena. Without linear equations, we will not be able to predict, establish, and study-specific phenomena.

## What are common everyday examples of linear equations in the real world?

Linear equations have many usages in everyday life. By using the standard form of a linear equations Ax + By = C and substituting it with different variables that we can find in real life. For example, you rent an apartment for an unknown amount of time that requires you to pay a base 500 USD rent + an increment of 25 USD per month. You can make a linear equation of 500 + 25m = X where m is the number of months you have stayed in the apartment and X is the total cost of the rent. With this, you can easily predict and estimate the overall cost of the rent you will have to pay using simple substitution.

## Can you put irrational numbers on a number line?

Yes, you can graph irrational numbers on a number line. Irrational numbers are real numbers that cannot be written in fraction form, unlike rational numbers. We can graph these numbers in a line because irrational numbers have specific values attached to them, even though they reach an infinite point. If we are to use π, whose value is 3.1415926…, and graph it into a line that reaches the value of one to five. Then π will rest in the points between the numbers three and four. If you want to even be more specific π will be located in the points between 3.1 and 3.15, drawing close to 3.15.

Linear equations are equations and solutions that describe the direct relationship between two variables or values. These two values are often represented by the letters X and Y, which can be solved to obtain four points that will create a straight line.