What is the Standard Form of a Linear Equation? | Functions and Relations, Forms of Linear Equations

What is the standard form of a linear equation? There are many different ways a linear equation can be written. From slope intercept form to point slope form, and of course today we go over another useful form that you will see a lot, and you will want to use, when solving systems of linear equations.

Standard form also makes finding the x and y intercepts of a linear equation fairly easy, and it works nicely for finding parallel and perpendicular lines through particular points! But we’ll leave all that for another lesson. Before we use standard form, we gotta know what it is, and that’s what we’ll go over in today’s video math lesson!

The standard form of a linear equation requires that all variable be on one side of the equation, and the constant be on the other side. You will find different articles or sites give different takes on exactly what simplification may or may not need to be done to complete the transfer to standard form, for example some sources might say you need to make the coefficient of x positive, or an integer, or any other number of things, but the important idea common to all ideas of standard form is that the variable terms are being added and or subtracted on one side, and the constants are on the other side. The importance of anything else you might want to do to clean up the equation will depend on the problem, but it can often be helpful to do some simplification like dividing by common factors or multiplying by a number to get rid of fractions.

Remember as well that linear equations are just equations with variables that only have exponents of 1, these equations can have more than two variables, and we touch on that in the video lesson. The standard form of a linear equation with more than two variables follows the same principles as the standard form of a linear equation with two variables. All the variable terms need to be getting added or subtracted on one side of the equation, and the constants need to be on the other side.

We also go over an example of going from slope intercept form to standard form, it's good fun!

SOLUTION TO PRACTICE PROBLEM:

1) We are given the equation y - 3 = 6( x - 3 ). Currently x is stuck in the parentheses, being multiplied by 6. So we carry out that multiplication first.

y - 3 = 6x - 18

Now we can subtract y from both sides (you could also subtract x from both sides but I like to keep my x coefficient positive).

-3 = 6x - 18 - y

Now we just need to get rid of the constants that are with our variables, in this case we have -18 on the wrong side. So let’s add 18 to both sides.

15 = 6x - y or, if you prefer: 6x - y = 15

We’re done!

I hope you find this video helpful, and be sure to ask any questions down in the comments!

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The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.

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+WRATH OF MATH+

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