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Standard Form of Linear Equations - Problem 2

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

To change an equation of a line written in point-slope form (y-y1)=m(x-x1) to standard form (Ax+By=C), start by distributing the term outside of the parenthesis and simplifying. Next, use inverse operations to bring x and y to one side of the equal sign and the constant to the other.

Here I have an equation that's given to me in point slope form. I want to go through, and turn it into standard form. Keep in mind standard form looks like this; ax plus by equals c. So my goal is going to be to get the xs, and ys on the same side of the equal side, and have my constant hanging out by himself on the other side.

So the first thing I need to do is some distributing, and simplifying. I'm going to rewrite this problem down here, so I have more space. Then let's go ahead and distribute on the right side to simplify. Distribute that -2, -8. Be really careful that -2 times 4 gives you the -8. Then let's combine the constants.

So now I have y equals -2x minus 5. Is there anything special in your brain? That's the y equals mx plus b or slope intercept form, but we don't want that. We've got to keep going. We've got to get it to standard form. I need to get this x term over there. So in order to do that I'm going to add 2xs to both sides, and then I'll be all set. 2x plus y is equal to -5. That's the same equation as this only written in different form.

So when your book or your teacher ask you to write it in standard form, it's just a matter rearranging everything so that you have your xs, and your ys together. Then your constant on the other side of the equal sign.

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