Linear Equation Formulas

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Graham Derreck

July 28, 2021 09:52

Greetings,

I am working my way through Algebra 1. Excellent learning resource! My question is to do with the use of the standard formula for linear equations. That formula doesn't seem to be as popular as it's point slope or slope intercept cousins. One reason given was absence of the slope. That is understandable.

I was reading that the slope could be determined from the standard formula using: m = -A/B. I was able to extract the slope using that my method and it agreed with the other formulas.

So it seems, by using standard, I can easily determine intercepts and slope. I am wondering the reason that: a-the standard form is not used as often as the other 2 and b-the use of -A/B to find slope is not mentioned at all.

I may be answering my own question here, but I also noticed that when extracting equations from a line, it seemed I was able to create either the slope intercept or point slope equations, but I had to extract the standard equation from one of the other 2.

Is it possible to extract the standard formula from the graph, and if so how?

I have had a life-long hatred of math...just kidding :). Let's call it pathological suspicion. I found this excellent site while studying for high school equivalency and I'm getting hooked.

Any help and guidance here would be most appreciated.

Thanks,

Graham

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Evan Lewis

July 30, 2021 18:03
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Hi Graham,

I think the main reason why slope-intercept and point-slope are the dominant forms used in the Algebra I course is due to ease of use and intuition. In my experience, most students find those forms to be more intuitive and prefer using them, at least when starting to learn linear equations. The slope and y-intercept can easily be extracted from slope-intercept form and point-slope form makes it easy to write an equation given only two points.

Additionally, when describing lines, slope-intercept form is the normal convention. If you use any sort of graphing tool or calculator, you'll see that this form is typically the default. Since standard form is essentially just a variation of slope-intercept, it's often times just an extra and unnecessary step to convert the equation into standard form, which is why this isn't normally done.

The one place where standard form is commonly used is in solving systems of equations, which is covered in the "Systems of equations" unit of the Algebra I course. When dealing with systems of equations, standard form becomes the default form and is covered/used a little more in this section.

I hope this helps clarify!
Graham Derreck

July 30, 2021 19:08
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Thanks Evan,

Excellent explanation.

Graham

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