What is a linear function? how do you use it?
356793
A linear function can refer to two slightly different concepts. In geometery and elementary algebra a linear function is a first degree polynomial mathematical function of the form:\n\nf(x) = m x + c \nwhere m and c are constants.\n\nThe problem with this geometric definition is that functions of the above form - despite their names - do not necessarily satisfy the conditions of a linear map. Therefore, some people refer to functions of the above form as affine functions. If and only if a function is of the above form with c equal to zero, the function satisfies the properties of a linear map, preserving scalar multiplication and vector addition for all points in its domain.\n\nLinear functions always have as domain the set of all real numbers and a range of all real numbers. By the geometric definition, the derivative of linear functions in terms of their independent variable, x, is always the constant m.\n\nLinear functions (according to the geometric definition) can also be written in the form:\n\ny = m x + c \nand plotted on an x,y graph. It forms a straight line, as the name implies.\n\nThe constant m is often called the slope or gradient while c is the y-intercept, which gives the point of intersection between the graph of the function and the y-axis.
141538
Read the references at the end of the article or talk to an industrial engineer.\n\nhttp://en.wikipedia.org/wiki/Linear_programming
665179
The linearization is the equation of the line tangent to f at x=a.\nThe point that L(x) is based on is (a,f(a)), which is (4,√13)\nFind the derivative of the function.\nf'(x) = 2x·[1/2√(x²+9)] = x/√(x²+9)\nf'(4) = 4/√13\nThe linearization:\nL(x) = (4/√13)x - 15/√13
1038364
Formula for linear slope is y=mx+b\n5y=10x-10\nDivide the 10x-10 and 5y  by 5 to get\ny=2x-2\n-21+7y=14\nAdd -21 to both sides to get\n7y=35 Hence y=5\nx=-5 The slope is undefined. IF you graph the line and take two coordinates and use the formulas (y2-y1)/(x2-x1) you get 0 at the bottom. Anything divided by 0 is undefined.\nY-5=2 is add the 5 to both sides to get y=7
1011462
You have two ways to do it...\nOne... if you have to do it on a graph paper... \nthen.. put some values of x and solve for y and make a table... and then plot those points on graph\n\nOtherwise.. use graph plotting softwares.. like gnuplot (which is a free software).. define function as f(x)=2x (f(x) is equivalent to y here) and say plot f(x).. it will plot you the function.
254599
Yes it is a function because the two variables have a 'one-to-one' relationship, which means that for  every value of x, you can get one and only one value of 'y'. If this one-to-one relationship exists then its called a function.\n  Ex.\n   If x=1, y=3\n   If x=23, y=47 etc.
730946
What do you mean by 'linear question?'\n\nThe disadvantage of using a calculator when trying to answer any question is that you do not learn effective problem solving techniques. I went through two semesters of Calculus without using my graphing calculator to solve any of the problems. I would use it to check my answers, but that's about all. Other people in my class used them to actually do their homework, and on the tests you could definitely tell. They could get the answers but, since my instructor wanted to see the work done, they would only get a fraction of what each question was worth. When I got into my third semester of Calculus, the problems we were working were much more difficult to solve. For these problems my instructor encouraged us to use our calculators to do the tedious work for us. Since we had already gone through the classes designed to teach us the material, he was confident that we knew how to do the math. What he was interested in teaching us was the more complicated process of understanding how to set up the problems so that we could get an answer with our calculators.\n\nSo, when you are just beginning to learn how to do problems it is better for you to do them by hand. You gain a much better understanding by doing this. Once you have been doing it for a while and are interested in applying what you have learned, that is when using a calculator is helpful. You can use it do to the calculations that you already know how to do and spend your time trying to learn the new material.
1048776
Type this in google\n\n   "linear programming.pdf"\n\n  U will get your answer on the very first page, with sites like these\n\n    http://www.stats.ox.ac.uk/~yu/
80482
This would most definitely be a polynomial function, since it starts with x cubed. Anything that has x cubed or higher in it, like x to the fifth power, would be a polynomial function. An equation with x squared would be a quadratic function. An equation with just x would be a linear equation.
101134
A function always outputs a value. Suppose the function \nf(x) = 10x+20, what this means is that this function outputs different values for different input values of variable 'x'. For example:\nf(10) = 10X10+20 = 120\nf(20) = 10X20+20 = 220\ni.e. we substitute different values into x and get different outputs. \nThe important point is that every function outputs a value.\n\nComing to Equations. Equations define the relationship between one or more variables.\nSingle variable equation:\nx2 - 10x = 0\nMulti vairable equation:\n2x+3y = 10\nAn equation doesnt output a value. We can solve the equation and find out the values of the variables. The equation would be valid only for certain values of the variables.\n\nHope the difference is clear.
706776
y is a function of x and in a linear way, so one can say that y is a linear function of x,\non the other hand, y=x+5 is a linear equation in 2 variables x and y.\n\nthe difference between function and equation is whether you can write a variable as a function of the other or not: for example:\nx^2 + y^2 =1 is an equation in 2 variables, but it is not a function... or more precisely you cannot get a function from it, since you would need to use the square root (at some point).\n!
978893
The last link was the most informative.\nThe function is as follows:\n(x' y')T = [(1 1)T (1 -1)T] (x y)T\n\nIf you multiply the basis vectors by this matrix you get:\n(0 2)T for the (1 -1)T vector and\n(-1 -5)T for the (-3 2)T vector.\n\n(0, 2) = c1 * (1, -1) + c2 * (-3, 2)\nso:\n0 = c1 - 3 * c2\n2 = - c1 + 2 * c2\nc1 = -6\nc2 = -2\n\nlikewise:\n(-1, -5) = c3 * (1, -1) + c4 * (-3, 2)\nc3 = 17 and c4 = 6\n\nM = [(-6 -2)T (17 6)T]
996164
Assuming A, B, and C to be constants, this is an equation that defines a linear relation between variables x and y. There are a number of places where this would appear, but it would be easier to see it in the form y = -(A/B)x + (C/B), its equivalent.
296652
Where's the function?
18487
A linear equation looks like a line when it is graphed.  The standard form of the equation is y=mx+b where m is the slope, and b is the value of y at the point where the line crosses the y-axis.\n\nA non-linear equation does not look like a line.  It may look like a curve.  A non-linear equation could possibly be a parabola, a circle, a wave, a hyperbola, etc... but not a line!
437570
You're probably talking about the vertical line test.  A relation is a function iff you can draw a vertical line anywhere and intersect the function at just one point.\n\nSo, something like y = x is a function because a vertical line always hits just one point.  y^2 = x is not a function because if you draw a vertical line at x=4, it hits the graph at both (4,2) and (4,-2).
612525
We can have a simple linear function such as F(X)= X times a Constant C. This type of function is used everyday when we convert "one thing" to "another". One currency to another (i.e. exchange rate); metric and a myriad of other conversions. How about taxes like the sales tax. You pay so much per gallon of gas; so much per unit of power used for electricity etc.\nHowever we can also have a function F(X1,X2,X3...Xn)= C which can be quite complicated and which is a function of many inputs X1,X2,X3....Xn. Such a function could be used in computer modelling for weather and economic forecasts, navigation, traffic control etc. hope that helps somewhat