How do you tell if an equation is linear?
962302
You tell an equation is linear if there's a simple relationship between "x" and "y".\n\nIf you can say that "y is 2 lots of x, plus some constant number" or "y is half of x plus some constant number", that's a linear relationship.\n\nNote that the constant number can be 0!\n\nWritten formally, that means y = ax + b, where "a" is the simple relationship and "b" is some constant number.\n\nIf you need to transform "x" in any other way, it's non-linear.
1161836
One way to write the equation of a line is\ny - y1 = m(x - x1)\nwhere m is the slope and (x1, y1) is a point on the line.\n\nGiven your information,\ny - 4 = -2(x - 1)\nThat is the point-slope form of the line.  This can be changed to slope-intercept form:\ny - 4 = -2x + 2\ny = 2x + 6
145305
Use cubic equation \ny=ax3+bx2+cx+d\n\nSince you have four points data you can get four linear equations with four variables which is very easy to solve, get variables (a,b,c,d) and plug the values to cross check and see u will get answer. Use guass jordan or elimination method.
89176
linear equatin is represented in the form of y=mx+c where m is the gradient of a graph and c is y intersection. traffic flow can be described as number of cars that use a road in a unit of time. if u plot the number of cars versus time, u will get a linear graph. find the gradient of the graph n find the y intersection, u will get a linear equation.
307198
It is linear on intervals, on (- infinite, 0) and on (0, +infinite) but not on the whole R. \n\nTry plotting it, you get a reversed V, not a straight line.
493962
depends\n\nif that is\ny = e^(x-1)\n\nor\n\ny = e^x - 1 (remeber no superscript!)\n\nthey are\n\nx = ln y + 1\n\nor\n\nx = ln (y + 1)
497371
http://en.wikipedia.org/wiki/Linear_equations\n\nhttp://en.wikipedia.org/wiki/Math
707230
A linear expression is an expression with ONE variable raised to the order of ONE (that is, the variable is not squared or anything). \n\nIt is important to distinguish between an EXPRESSION and an EQUATION. An equation occurs when something is equal to something (e.g. 1=1, states that 1 is equivalent to 1). \n\nAn expression is simply a string of variables and numbers that represent ONE number (e.g. 1+1, which represents 2). You can tell between the two by the presence of an equal sign (=).\n\nFor example, \n\n1 + x is an EXPRESSION whereas,\n\n1 + x = 2 is an EQUATION. \n\nThe expression 1 + x does not mean a definite number. It is very much like a variable; it can equal just about anything since it simply acts as a placeholder. An equation, on the other hand, explicitly states that the expression is equal to something, thus giving the variable a value.\n\nYou may think of it as a lock and a key. An expression is like a lock, it is simply there and has no meaning until both lock and key are present (equation).\n\nNow, consider your expression 4a + 7 - 2a + 3. The expression, like a lock, is simply there. It has potential, but means nothing. The entire thing could very well be a variable x, and still mean the same thing.\n\nHowever, the expression can be simplified, much a 1 + 3 + 4 can be reduced to 8 (though it will not actually be a number). Gather the like terms (4a - 2a) + (7 +3), then simplify individually:\n2a + 10. This expression is equivalent to the original, and simpler.
417878
linear.  Linear means "to the first power", nonlinear means "to the second power (squared)", "to the third power" or higher (or some other function).  \n\nPerimeter of a square = 4 x length of side.\nwhich means \n4 x "length of side to the first power"\n\ndouble the length of the side and you double the perimeter; triple it and you triple the perimeter.
869931
You need to show that the only way to make a combination of them sum to zero is for all the multipliers to be zero.  For instance, say you have three vectors x, y, and z .  Then you need to show that if \n\nAx + By + Cz = 0 \n\nis true, then A, B, and C must ALL be equal to zero.  That is, the only way for the above equation to be true is if all the coefficients are zero.  If you can find a set of A, B, and C that satisfy the above equation, then the vectors are NOT linearly independent.
743347
It all depends on what result you're hoping to get.  For example, if you want to solve a system of equations in two variables, you would try to get the variables on the same side in both equations.  If you want to express the equation in slope intercept form, you would move the y variables to the left side and the x variables and constants to the right side of the equation.  If you're trying to express the equation in standard form, i.e. ax + by + c = 0, you want both variables on the same side.
471523
A linear equation in two variables describes a relationship in which the value of one of the variables depends on the value of the other variable. In a linear equation in x and y, x is called x is the independent variable and y depends on it. We call y the dependent variable. If the variables have other names, yet do have a dependent relationship, the independent variable is plotted along the horizontal axis. Most linear equations are functions (that is, for every value of x, there is only one corresponding value of y). When you assign a value to the independent variable, x, you can compute the value of the dependent variable, y. You can then plot the points named by each (x,y) pair on a coordinate grid. The real importance of emphasizing graphing linear equations with your students, is that they should already know that any two points determine a line, so finding many pairs of values that satisfy a linear equation is easy: Find two pairs of values and draw a line through the points they describe. All other points on the line will provide values for x and y that satisfy the equation.\n\n\nA linear equation is special because: \n-It has one or two variables. \n-No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. \n-When you find pairs of values that make the linear equation true and plot those pairs on a coordinate grid, all of the points for any one equation lie on the same line. Linear equations graph as straight lines.
176944
the standard form is: Ax + By = C\n\nin your two equations you dont have any 'y' so you might have typed it wrong but if it is right then 'B' is 0.  \nthen combine like terms. this should leave you with Ax + (0)y = 0\n\n\nto determine 'x' and 'y'...\n\n             PART #1\n1. choose 'x' as zero\n a. this eliminates 'Ax'\n2. divide both sides by coefficient of 'y'\n a. this leaves y = C/B\n3. determine y\n\n             PART #2\n1. choose 'y' as zero\n a. this eliminates 'By'\n2. divide both sides by coefficient of 'x'\n a. this leaves y = C/A\n3. determine x\n\ni hope this helps!
974911
To answer this I must first explain what an equation is:\nAn equation is where 2 sides are equal to one another.  Ex. 4x + 13 = -91\n\nAn expression does not have the = sign.  Example: 4x + 13
1102588
Nonlinear is a term used to relate one property to another. If the two properties are related so that a change in one property causes the other to change proportionally, they are linear. One way of looking at this is if you were to graph one versus the other, you would get a straight line with the slope being the ratio of the rate of change of one compared to the other.\n\nFor example, solids, liquids and gases tend to expand proportionally to temperature.\n\nProperties are nonlinear if they are not proportional to each other. For example, if one varies as the square root of the other, or the second or third power of the other, they are nonlinear.\nAir has many properties that are nonlinear. For example, the speed of sound in air is nonlinear when compared to the air temperature.
130030
linear operator takes a vector and maps it into another vector while preserving addition and multiplication by a scalar:\n\nL(ax+y)=aL(x)+L(y)\nx,y are vectors, a is a scalar, L() is operator\n\nIt can be defined by a matrix, i.e. result of operator is given by multiplying that matrix by a vector.\n\ngo look it up on wikipedia.org or mathworld.wolfram.com
940602
You're correct. Differentiating them and showing they are equal to zero will indicate that they are constant. The equation\n\nA(w_1)^2 + B(w_2)^2 + C(w_3)^2\n\ndifferentiated with respect to time yields\n\n2*A*w_1*(d/dt w_1) + 2*B*w_2*(d/dt w_2) + 2*C*w_3*(d/dt w_3)\n\nIf you substitute from the system of equations that shows the evolution then\n\n2*w_1*w_2*w_3*(B-C) + 2*w_1*w_2*w_3*(C-A) + 2*w_1*w_2*w_3*(A-B)\n\nyou can see that the terms cancel leaving you with zero.\n\nFollow the same technique for the second equation. It will look similar except you will wind up with an additional constantt, e.g., A*(B-C), etc.