why is y=mx+c?

Question

give me detailed reasoning and proof

Answer 1

y=mx+c is the algebraic statement of locus of points of a straight line or a set of points that is thought off as arranged in the form of a straight line. Actually, given equation gives the ordinate of a single point in the set of straight line, with respect to the given value of `x' and a constant values of c& m. Co-ordinate Geometry or Analytical Geometry, Algebraic Geometry is the systematic study of position of a point in space using algebra with respect to the frame of reference called co-ordinate axes that are denoted by x, y, z. In the given equation y represents the ordinate of the point on the straight line, m is the slope in which the set of points arranged in a straight line, and c is the y intercept of a straight line. It is true that every straight line in a bi-dimentional space intersect the frame of reference axes at two points x & y , except at the origion. Abcissa and ordinate of these intersecting points are constants w.r.t the straight line. Therefore it is denoted by c. Herein the given equation, c is the y intercept because x is the variable referance position on abcissa. The confusing factor here is y & c as both are ordinates. But it has to be noticed here that y is the ordinate of any point on the straight line where as c is the ordinate of only point that is intersecting the y axis. To make it more clear, I would like to furnish a presumptive example as following.
Think off high towers one in front of the another. second tower is higher than the first one. A TV cable is tied tightly at the top of the towers in the form of a straight line. Given height of the first tower is 2 units, slope of the cable that is considered as straight is 0.5 and distance between the towers on the ground is 2 units. To find the height of the tower y=mx c can be used.
ie.considering first tower and the ground as the frame of reference, we have c=2, m=0.5 and x=2 , y=height of the second tower.
Substituting these data in y=mx c
We have, y=0.5*2+2=3 units
Height of the second tower is 3 units.

Answer 2

It depends on how basic you want to be: a line can be defined (the way it is inclined, and where it is) by mapping it on a background of squares, and pointing out the relationship between the numbers assigned to the squares left to right, and the numbers assigned to the squares up and down. If you have the corner of one square labelled as zero along and zero up, all the points on a line can be identified by (p,q) where p is the left/right number from zero-zero, and q is the up/down number from zero-zero. It works out that if (0,0) and (2,4) are both points on a line, then (5,10), (9,18),(200,400) are further examples of points on the same line. The left-right direction is called "the x axis" and the up-down direction is called "the y axis". In the example I make above, ALL the points are in the form (k, 2k). There is always a direct relationship between the x and y "coordinates" (numbers) in a line. This means that if somebody tells you the nature of a line and then the x coordinate, you should be able to calculate immediately the y coordinate for thazt point on the line: in our example, the nature of the line is that y = 2x. Every line that goes through the zero-zero point (called "the origin") is of the form y = mx where m is a value that gives you the relationship. if m is zero, y will be zero for every point -- which means the line will be horizontal, straight through the origin. If m is 1, the line is a diagonal going upward to the right, at an angle of 45 degrees. For larger m, the line goes upward to the right at an ever steeper angle. Of course, m can be negative -- which means that the line goes up the the left. So far we have only considered y = mx, where m affects the steepness and direction of the line, but it only applies to lines going through point (0,0), the "origin". The value of m can be anything, positive or negative. If we modify the general expression by incorporating a constant, we can specify other lines, not going through the origin. Suppose we want to define a line with slope 1 (which is 45 degrees upward to the right) that goes through point (0,c) we can instantly say that its algebraic formula is y = mx+c. So the definition of a line in x/y coordinates is (y = mx+c). When the line has been fully defined, the m and c are replaced with actual values. Any general line can be described by the formula "px + qy + r = s" where p,q,r and s are known values. This can be switched around into the (y = mx + c) form easily:
m = -p/q and c = (s-r)/q. Both are equally valid ways of defining a line, but (y=mx+c) tells you immediately the most commonly useful details.

Answer 3

hmmm... the way I remember it.. is y = mx +b where x is a value on the horizontal or independent axis, y is a value on the vertical or dependent axis, m is the slope of the line, and b is the value of y when x = 0 (called the y-intercept).

x and y axis variables.. are defined... so there is no proof.. you can call them whatever you want to call them... just so they are at right angles on a flat plane.

m is the slope.. which is defined as rise/run... or (change in vertical)/(change in horizontal)... can't prove that.. it is a definition again

b is the value of y when x is zero.. hmmm.. if you have values for x, y, and m... then you plug them in.. and solve for b

Answer 4

Here Y is dependant variable. X is independant variable. m is the magnitude of the independant variable or SLOPE of the line. C is the point of intersection of the line with Y axis. The m (slope) may be calculated by tan A, where A is the angle with which the line intersect the X axis. Some times, m can be measured by dy/dx.

Answer 5

slope of a line:

y=mx+c because according to its author it the way to solve a slope of a line, given the values and etc.. you can create your own formula and values and yet youll end up having the same answer with this y=mx+c... this formula was already proven and defended by its author and now whether we like or not part of mathematics.. unless you decided not to use it...

Answer 6

there is nothing to reason out or prove. y=mx+c is a linear function n can also b considerred as a line equation with slope "M"

Answer 7

It is the equation of a straight line.
You can find good proofs only in books.

Answer 8

Wow I guess you think your smart mr Algebra guy.
While you were worried about Y, some dingos ate your baby.
I hope your satisfied.

Answer 9

coz that's the way it is.
by the way its a straight line cutting intercept c on y axis and havig slope m

Answer 10

It seems like a linear function. No need to prove it is right cause there's nothing to prove.