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## Algebra 1

### Course: Algebra 1 > Unit 5

Lesson 5: Standard form- Intro to linear equation standard form
- Graphing a linear equation: 5x+2y=20
- Clarifying standard form rules
- Graph from linear standard form
- Converting from slope-intercept to standard form
- Convert linear equations to standard form
- Standard form review

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# Clarifying standard form rules

Clarifying standard form rules.

## Want to join the conversation?

- Why do some mathematicians want the real number A in standard form to be greater than zero?(18 votes)
- In Math (or science in general), rules are made to help avoid confusion and make things as simple as possible.

Mostly likely, the people saying that they want a integer (A, B, C), non-negative (A), simplified equation is to make the equation easier to understand and better for our purposes.

When it comes down to it, in everything different people have different views for why things are simpler and work better. In Math, sometimes Mathematicians thinks one way works best, but in this example (like Sal said), there is actually some debate on what is best, and it is mostly up to you (and your curriculum) as to what you use.

Hope this helps,

- Convenient Colleague(8 votes)

- Why isn't there universal rules that dictate such a standard?(10 votes)
- There aren't universal rules because such would require vast groups of mathematicians to unite and create a standard rule. You could find one type of equation and find that it is done in numerous different ways depending on the country. Besides, most mathemeticians believe their method is most efficient, if only because they have not learned other methods and do not care to learn those methods. The world of Math lacks conformity and unity in many branches.(10 votes)

- I need help with this problem.

I have the equation y=2x+8.

I don't know if I can change it into standard form.(5 votes)- If you want x coefficient to stay positive, subtract y from both sides and 8 from both sides to get 2x - y = -8.

If you do not care about the sign of x coefficient, subtract 2x to get -2x+y=8.(12 votes)

- Which variable in standard form represents the slope?(4 votes)
- Variables do not define slope, coefficients of the variables define slope. So slope intercept form is easy, y=mx+b, so the coefficient of x is the slope. In standard form, Ax + By = C, we subtract AX to get By = -Ax + C, divide by B to get y = -A/B x + C/B. So the slope is the negation of the coefficient of x divided by the coefficient of y.(7 votes)

- As for the standard form rules, I have a test coming up and I don't know to follow these rules or not.

And I really want to pass my test.(3 votes)- It can never be a bad thing to follow standard form rules, but you could possibly loose points if that is the expectation. The biggest mistake students make in shifting to standard form when necessary is the negative signs, so you need to think of the coefficient of a variable as being negative or positive, not just that there is a negative sign. So if you end up with y = 3 - 2x, the coefficient of x is -2, so if you put in slope intercept form, it is y = - 2x + 3 (the wrong way is to say y = 2x - 3 which is a different equation).(6 votes)

- what does c stand for?(4 votes)
- C is just the constant term which is on the right. If you divide C/B, you get the y intercept.(4 votes)

- What if your only are given to points, for example: What is the equation of a line, in general form, that passes through points (-1, 2) and (5, 2)? And is general form the same as standard form?(3 votes)
- If general form is 0 = Ax+By+C, no that is not the same as the standard form for linear equations.

Since what you described is a zero slope line so for a clearer example let's use two different points: (-2,3) and (1,12)

Using the slope formula we can identify the slope:

(y2-y1)/(x2-x1)

(12-3)/(1-(-2)) = 9/3 = 3

Now we have m = 3 — perfect.

Now we will utilize the**point-slope formula**, which is:

y - y₁ = m(x - x₁)

Let y₁ be any given y coordinate and x₁ be any given x coordinate

Let's use (1,-2), but you can use either or coordinates.

y-2 =**3**(x-(-1))

y-2 = 3(x+1)

y-2=3x+3**y=3x+5**

That's the equation given only 2 points !

More on point-slope formula:

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:point-slope-form/v/point-slope-and-slope-intercept-form-from-two-points(5 votes)

- Why does standard form even have these rules? Why does it matter if A B and C have a common factor and that they have to be integers? Is it just because or is there a legitimate reason?(3 votes)
- In Math (or science in general), rules are made to help avoid confusion and make things as simple as possible.

The reason why some say that A, B, and C can't share any common factors is because they want Standard Form to be completely simplified, so that it is as clean as possible.

I'm sure there are other reasons for why some people want to exclude A being negative; and A, B, and C being integers.

When it comes down to it, in everything different people have different views for why things are simpler and work better. In Math, sometimes Mathematicians thinks one way works best, but in this example (like Sal said), there is actually some debate on what is best, and it is mostly up to you (and your curriculum) as to what you use.

Hope this helps,

- Convenient Colleague(4 votes)

- does the leading coefficient in a standard form linear equation have to be greater than zero?(3 votes)
- No, not always. Sometimes, there can be a negative coefficient. It really depends on the question, or what you with it. However, "A"
**should**always be positive, in the standard form linear equation.

Hope this helps.(4 votes)

- What do you do if you don't know what A stands for?(3 votes)
- Not sure what you mean by this, it this application, A is the coefficient of x, B is the coefficient of y, and C is the constant term.(4 votes)

## Video transcript

- [Instructor] We've talked about the idea of standard form of a linear
equation in other videos, and the point of this video
is to clarify something and resolve some differences
that you might see in different classes in terms
of what standard form is. So everyone agrees that standard form is generally a linear equation where you have some number times x plus some number times y
is equal to some number. So things that are in
standard form would include things like three x plus
four y is equal to 10, or two x plus five y is equal to negative 10. Everyone would agree that
these are standard form, and everyone would
agree that the following are not standard form. So if I were to write three x is equal to negative four y plus 10. Even though these are
equivalent equations, this is just not in standard form. Similarly, if I wrote that y is equal to three times x plus seven, this
is also not in standard form. Now the place where some
people might disagree is if you were to see something like six x plus eight y is equal to 20. Now why would some folks argue that this is not standard form? Well, for some folks, they
would say standard form, the coefficients on x and
y and our constant term, so our A, B and C, can't
share any common factors. Here, six, eight and 20,
they're all divisible by two, so some folks would argue that
this is not standard form, and to get it into standard form, you would divide all of these by two, and if you did, you would
get this equation here. Now that's useful because
then you only have one unique equation, but on Khan Academy, we do not restrict in that way, and that is also a very popular
way of thinking about it. We just want you to think
about it in this form, Ax plus By is equal to C. When you do the exercises
on the Khan Academy, it's not going to be checking
whether these coefficients, A, B and C are divisible,
have a common factor. So for Khan Academy purposes, this is considered standard form, although don't be surprised
if you encounter some folks who say, no, we would rather
you remove any common factors. Now another example
would be something like negative three x minus four
y is equal to negative 10. So some folks would argue
that this is not standard form because they want to see
this first coefficient right over here, the A,
being greater than zero, while here it is less than zero. For our purposes on Khan Academy, we do consider this standard form, but I'm just letting you know, because some folks might not because this leading coefficient
is not greater than zero. Now another example that
some people might be on the edge with would be something like 1.25 x plus 5.50 y is equal to 10.5. The reason why some people
might not consider this standard form is that A,
B and C are not integers. Some folks would say
to be in standard form, A, B and C need to be integers, and you could multiply
both sides of the equation by some value that will give
you integers for A, B, and C, but for Khan Academy purposes, we do consider this to
be in standard form. We think this is important, actually not just being
able to have non-integers as A, B or C, but also being able to have a negative A, right over there, because negative three is our A, and also having coefficients,
having our As, Bs and Cs having shared factors, we
thing all of that's important because sometimes the
equation itself has meaning when you write it that way. We'll see that when we
do some word problems, when we actually go into some real life and we try to construct equations, and based on the
information in the equation, it's easier to understand
if you keep it in this form. So for Khan Academy purposes,
this is all standard form, but it's good to be aware
in your mathematical lives that some folks might want
to see the restriction of no common factor between A, B and C, that A is greater than zero, and that A, B and C
need to all be integers, but Khan Academy does
not hold you to that.