How to Write an Equation in Standard Form

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  • 0:04 Equivalent Equations
  • 2:01 Linear Equations in…
  • 3:11 Polynomial Equation…
  • 4:22 Lesson Summary
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Lesson Transcript
Instructor: Laura Pennington

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

This lesson will go over equivalent equations and how to use the rules of equivalent equations to write an equation in standard form. This process is extremely useful when you are working as a team member on a specific problem.

Equivalent Equations

Imagine this: you're working with two other students, Andrea and Susan, on a problem in math class. You are trying to find an equation to represent a word problem. You all work separately to solve the problem and then compare answers. You came up with the equation 2x - y = -1. Andrea came up with the equation y = 2x + 1. Lastly, Susan came up with y - 3 = 2(x - 1) as her equation. You all think that your answer is correct, so why did you all come up with different answers? You go to ask the teacher, and the teacher tells you that, in fact, you are all correct! What? How are you all correct if you got different answers?

The answer to this conundrum lies in equivalent equations. Equivalent equations are equations that have the same solution set, but may look different. When it comes to equivalent equations, you can manipulate one equation to make it look exactly the same as the other equation. For example, consider yours and Andrea's solutions. Andrea got y = 2x + 1. Try subtracting 2x from both sides of that equation, and then multiplying both sides by -1, which you can see playing out below:


standard11


You see that you can manipulate Andrea's equation to become your equation. You can do the same with any two of the equations that you three came up with because they are all equivalent equations. The following rules of equivalent equations show how we can manipulate an equation to produce an equivalent equation in the form we would like.


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There are many different ways to write an equation. We are going to concentrate on just one way of writing an equation, and that's in standard form. Starting with linear equations, let's look at how to write an equation in standard form.

Linear Equations in Standard Form

Linear equations are equations that, when graphed, form a line. The highest exponent of any variable in a linear equation is 1. You can see some of the examples below:


standard3


Notice that the equations that you, Andrea, and Susan got are linear equations. The standard form of a linear equation is as follows:


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In the standard form of a linear equation, the A should be positive, so if you get it into standard form and the A is negative, multiply both sides of the equation by a negative to make it positive.

This tells us that if we want to put a linear equation in standard form, we must manipulate the equation so that the left-hand side of the equation has the x and y terms, with the x term coming first, and the right-hand side of the equation has a constant.

Look back at the three equations you and your friends came up with in our example. Which one is in standard form?


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If you said your equation was the one in standard form, you are correct! Notice that when we manipulated Andrea's equation to put it in the form of your equation, we were actually putting Andrea's equation in standard form using our equivalent equation rules.

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