How to Solve a Linear Function

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To solve a linear function, which usually means solving for Y, isolate Y on one side of the equation by moving the other terms to the opposite side and simplify the equation until Y is solved. Solve a linear function, which can easily be graphed, with information from a standardized test prep instructor in this free video on education.

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Let's talk about how to solve a linear function. So here's a linear function. So if we want to solve this linear function--so first of all linear, by the way, is just a fancy word for line; you can even hear it: linear, line. So linear function is a function that when you graph it it's going to look on your graph like a line. And that's the kind of function you do most in like algebra one, you deal with linear functions quite a bit. So if we want to solve this--ordinarily if your teacher asks you to solve it, what they mean is solve for y. And the reason is because when we get it into the form y equals something, it makes it very easy to graph. You might be asked at some point to solve for x, you could do that also. So when we want to solve for y, we want to get y alone; solve for y means get y alone. So we're going to move everything else away so that y is by itself. First we're going to subtract two x. Two x minus two x cancels--that's why I did it. You know if you have positive two x you subtract two x. You're going to do the opposite to get rid of it. This thing, which is really the equivalent of plus two x, the way that we eliminate it from this side is to subtract two x because then we get zero; it's gone. And of course whatever you do on one side of the equation, you have to do to the other. That's the law of equations. Once you know that, actually, equations are pretty easy. So that's done. So we get three y by itself equals--now we have nine minus two x. I'm actually going to write negative two x plus nine. I could have written nine minus two x--now by the way those are not like terms, so we're not going to combine them; they don't combine. If it had been nine x and two x they could combine. I put the two x first only because when we have y equals m x plus b that's the easiest form to graph in, and it's usually the one your teacher is looking for. So you're going to put the x first. Notice that the negative sign stayed with the two x; it belongs to the two x. Now I'm going to divide both sides by three. Why do I do that? Because this is three y; it's like saying three times y. And when you want to get this away, when you want to eliminate that, you do the opposite. The opposite of addition was subtraction. The opposite of multiplication--these are being multiplied--is division. So I divide by three, and I need to do that to everybody. Whatever you do to one side, you have to do to both sides of the equation. And you have to do it to all members of that side when you're dividing. So I get--that cancels, that's why we did it, three over three cancels--I get y alone equals negative two thirds x plus, and in this case it reduces: nine over three, nine divided by three, is three. So if I want to solve for y in this linear function, my answer is y equals negative two thirds x plus three. The two things to remember: whatever you do to one side of the equation you have to do to the other, and when you're trying to eliminate something from one side you do the opposite. In other words if it's being added, you subtract. If you have two things being multiplied together then you divide. And that's how you solve a linear function.

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