Please help question on standard form of a line?

Question

here's my problem i have a few teachers who taught me "standard form" is "y=a+bx" , and 1 who reacently taught me that it is "Ax+By=C"..... which one is correct? back up your answer too please

Answer 1

y = mx + b is "slope-intercept form". Sometimes it's called standard form, because it's the easiest form to use for graphing.

However,
Ax + By = C is the real Standard Form.

This has a very good explanation:
http://mathforum.org/library/drmath/view/60548.html

Basically,
Ax + By = C is Standard Form because every line can be written in that form.

Not every line can be written in slope-intercept form (y = mx + b). For example... a vertical line can only be written in the form x = #. So, those can't be written in slope-intercept form.

Note: x = # is the same as
1x + 0y = # - which would be a little redundant, but in the "standard form".)

Answer 2

They're both correct. They are just two different forms of the same equation:

1) Ax+By=C
2) Bring the Ax over: By=C-Ax
3) Divide by B: y=C/B-A/Bx
4) Since the letters are nothing more than labeled constants, they can be relabeled and you get an equation in the form of: y=A+Bx.

Typically, having y=... is the standard form of a line.

Answer 3

prevalent variety for a linear equation is: Ax + via = C least complicated thank you to sparkling up it is slope variety equation. y=mx + b m = slope and b = the y intercept. y = -7/8x + b locate the place the line crosses the y axis, i.e. x = 0. locate the factor (5,2) on a graph and notice that a adverse slope line would desire to upward push (helpful) boost because it strikes in a adverse x course in the direction of the y-axis. y = b = 2 + (- 5) *(-7/8) = 2 + 4.375 = 6.375 y = -0.875x + 6.375 convert to prevalent variety: 0.875x + y = 6.375

Answer 4

Standard form is Ax+By=C
Slope-Intercept is Y=mx+b...............m is the slope, and b is the y-intercept. You can use different letters for the variables, if your teacher says it's okay.

Good luck! Algebra's confusing sometimes, but you'll get it.

Answer 5

i have always been taught: y = mx + b where m is the slope and b is the y-intercept..

in your first eqn, b is the slope and a is the y-int.

I have never personally seen the 2nd one as a standard form of a line, I have always used the y-int form --- although the 2nd eqn is correct, just cluttered..

Answer 6

standard form is y = mx +b
which is useful because it lets you see the slope (m) and the y-axis intercept

Now the intercept form:
ax + by = c
is another way to to describe a line. This way will let you see the intercepts with both axis.

Answer 7

They are both correct although I would think that y = mx + c is that most commonly used.
y = mx + c corresponds to your y = a + bx.
Ax + By = c can be changed to
By = - Ax + c
y = (- A/B)x + c / B
y = m x + C
where m = (- A/B) and C = (c / B)

Answer 8

They are both correct. However, in the y = mx + b form, it is much easier to spot the slope and y-intercept.

So, the answer is: "Choose whichever your teacher prefers."

Answer 9

They are the same. Just follow along as I rearrange them...
Ax+By=C
By = C - Ax
By = C + (-A)x
y = (C/B) + (-A/B)x
let (C/B) = a
let (-A/B) = b
so then you get what your other teachers have shown you...
y = a + bx

The different forms are used depending on their purpose, for example in geometry or linear algebra.

Answer 10

standard form is ax+by=c
where a, b, and c are nonzero numbers

Y-Intercept form (whichi i think the one you are thinking of) is
y=mx+b
where m=slope
b=y-intercept

y-intercept equations can be manipulated into standard form easily.