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Can anyone has proof for slope-intercept form(y=mx+b)

Mathematics
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urgent!!! i have a seminar plzz

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Other answers:

@hartnn @hba plzz help
its just a form of equation of line....it cannot have a proof....but other forms can be converted to this form y=mx+b using some arithmetic.
and i am not typing... ha ha ha ..
y=mx+b is a equation of a line or slope intercept form??
y=,x+c is the slope intercept form of equation of line...
y=mx+c what is c?
y=mx+c or y=mx+b b or c is called 'y-intercept'
i think its y=mx+b not c
then b is y-intercept
ohkkk!!
it has'nt proof? right @hartnn
right???
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so
lets say, P(x, y) is some point which lies on this line with slope m and y intercept = c, then the slope = m = (y-c)/x mx = y-c y = mx+c thus the point (x, y) on the line with slope m and y-intercept c lies on the line if and only if y = mx + c
We know : \[m = \frac{y - y_1}{x-x_1}\] \[\implies m(x-x_1) = y - y_1 \implies mx - mx_1 + y_1 = y\] Here : \(y_1 - mx_1 =b = y- Intercept\) \[\color{green}{y = mx + b}\]
then the slope = m = (y-c)/x how did you get?? @ganeshie8
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3 statement ?????confused???? @waterineyes
not satisfied?? @ganeshie8 plz explain me step by step
do u knw the slope formula ?
Here : --------- INTERCEPT how did you get? this line
@ganeshie8 take that 'c' as b...
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right? @ganeshie8
right. u seeing 2 points on that line ? apply slope formula to those two points, and see what u get
point1 : (0, c) point2 : (x ,y) slope = m = ?
@Hares333 : \(y_1 - mx_1 = b\) Becuase, in y-intercept, x_1 must be 0, so we are left with : y_1 = b = Intercept..
See, I am taking the example of @ganeshie8 : He has taken : \((x_1,y_1)\) as \((0,c)\). Now : \(y_1 - mx_1 \implies c-0 \implies c\) And \(c\) is nothing but y-intercept..
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Yes go ahead...
You can write "Slope" as m..
1 question arise!!! is that What is the slope-intercept form..
Slope Intercept form is what you are asking this question For...
what's the diiference betweem slope-intercept form and equation of a line?
We call 'm' as Slope and b or c as y-Intercept or simply Intercept.. So , this makes Slope-Intercept Form..
and what about equation of a line?
Slope-Intercept Form is the method for finding equation of a line... It is a way to find a line equation...
Equation of Line represents that In 2 or 3-Dimensions, what are its dimensions.. How long it is along x-axis, how long it is in y-axis and z-axis etc etc...
very-very thank you @waterineyes you are a gr8 helper!!!
You are welcome dear...
And @hartnn , this time I am typing.. Ha ha ha ha..

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