If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Algebra 1>Unit 5

Lesson 5: Standard form

# 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?
• 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
• Why isn't there universal rules that dictate such a standard?
• 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.
• 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.
• 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.
• Man, I wish one day " math " will finally grow up and solve its own problems (-_- )
• Which variable in standard form represents the slope?
• 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.
• 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.
• 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).
• what does c stand for?
• C is just the constant term which is on the right. If you divide C/B, you get the y intercept.
• 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?
• 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:
• I think ima fail the eoc for algebra.
• 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?
• 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