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Standard Form of a Line - Concept

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

We will commonly see lines expressed standard form, especially when we look at and write systems of linear equations. The standard form of a line puts the x and y terms on the left hand side of the equation, and makes the coefficient of the x-term positive. While standard form is commonly, we sometimes rewrite a line in slope-intercept form in order to graph it.

So standard form of a line is probably the least practical form of a line but it is something that we see from time to time so it is good to understand how it is used. So what standard form is, is an equation of the line ax+by=c. And what has to happen for this form [IB] is ab and c have to be integers, so they have to be whole numbers. b and c can be positive or negative but we also know that a has to be greater than 0. Actually a could also be 0 in case it's a special line. So we know that this first term has to be positive and every other number has to be a integer.
Okay, so one example of how this could work is, we have y=-1 half x+7, 6. And we're asked put this in to standard form. Okay, so what we have to do is we first have to make our coefficients whole numbers. Okay, so we need to get rid of all of our fractions. And the way we do that is by multiplying by our least common denominator. So in this case our least common denominator is 6. Multiply everything by 6. That 6 goes to the y, 6 goes to the negative -1 half and to the 7, 6 we're left with +7.
Next thing we need to do is make sure our coefficient on x is actually positive. So right now it's positive which means we have to bring it over to the other side. So we add it over, 6y+3x=7, just a little bit of rearranging cause our x term is supposed to be first, 3x+6y=7. These are the exact same line. This one you know is in slope intercept. This one is in standard.

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