Kim has a Ph.D. in Education and has taught math courses at four colleges, in addition to teaching math to K-12 students in a variety of settings.
The standard form is simply a particular format for writing an equation of a line. It looks like this:
Ax + By + C = 0
The key is that the x part comes first, the y part comes next, and the constant, or C (the number without an 'x' or 'y'), comes last.
For example, if A = 2, B = 3 and C = 3, the standard form would look like:
2x + 3y + 3 = 0
Why Standard Form Matters
Looking at equations in standard form can be very helpful. In mathematics, when an equation is a line, it simply means that you have two things that vary - maybe the number of swings on a playground at the local elementary school and the number of Band-Aids the principal needs for students who fall off the swings in the month of October. But, more importantly, those two things have a consistent and precise relationship. If there are 2 swings, the principal will need 13 Band-Aids in October. If there are 5 swings, he will need 25. If there are 9 swings, he will need 41.
Given these numbers, the relationship between Band-Aids and swings may seem a little confusing. In fact, you may wonder whether there is a consistent relationship at all. A verbal description of the rule used to get from swings to Band-Aids may help: multiply the number of swings by 4 and add 5 to get the number of Band-Aids needed. Stating the rule clarifies the relationship.
Another way you might clarify the relationship is like this:
Band-Aids = 4 x swings + 5
Band-Aids - 5 = 4 x swings
Band-Aids - 4 x swings = 5
- 4 swings + Band-Aids - 5 = 0
-4 x+ y - 5 = 0 (where x represents swings and y represents Band-Aids).
All of those four equations represent the same relationship. Nothing is wrong with any of them. The last one is in standard form.
Why does this matter? Well, pretend there are two schools in your neighborhood - Oak School and Maple School. Oak School's swing to Band-Aid formula looks like this:
y = 2x + 1
Maple School's formula looks like this:
-2x+ y = 1
Are they the same, or are they different? With a little algebra, you would discover that they are the same - just rearranged. When graphed, they both indicate the line shown.
Using a rule for how to write the formula makes comparison faster and easier. It's like trying to figure out which newborn puppy is bigger. If they have wiggled into all sorts of directions, it is nearly impossible. Line them up the same way and get them to hold still, and comparisons become much easier.
Other shapes, such as circles, ellipses, and parabolas, also have standard forms. In some cases, the standard form is not only useful for comparison purposes but also allows for picking out certain parts of the shape, such as the center, more easily.
The standard form of a line is a set way of writing a line's equation so that the x part comes first, the y part comes next, and the constant (the number without an x or y) comes last - but all are on the left hand side of the equation with a zero on the right.
As you learn about standard form through this lesson, test your ability to:
- Illustrate the standard form of an equation
- Use standard form and recognize its importance
- Point out the fact that additional shapes have standard forms
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