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Is following function linear? f(x) = k {y / (k -y)} where k is a constant, x and y are variable, k >y

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Jomo said: If c≠0 Click to expand... Then c doesn't exist. Would you or anyone write y = 3x + 0 ? Yes it's true that in reference to graphic plots linear only means a straight line through the origin.
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studiot said: Well y = mx + c is not linear for a start. Click to expand... If c≠0
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greg1313 said: m and c are variable constants. x is raised to a non-negative integer. That is an equation for a line (linear relationship). Click to expand... Since 3 is a non-negative integer, then according to you y =mx^3 + b is linear. Most people would say it is a cubic.
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Consider the function f(x) such that y = mx + c The definition of a linear function is βf(x) = f(βx) Substituting into left hand side βf(x) = βmx + βc Substituting into right hand side f(βx) = βmx + c So the linear function definition condition is not satisfied and the function y = mx + c is not linear. It is still a straight line and is called 'affine'. In science and some elementary maths this difference is too often ignored and the function called 'linear', because it is a straight line. This is why CaptainBlack asked for the definition of linear given to the OP. This distinction may appear nit picky and trivial, but it is the reason that Newton's Laws of Motion as usually stated do not obey The Principle of Relativity.
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studiot said: Well y = mx + c is not linear for a start. Click to expand... m and c are variable constants. x is raised to a non-negative integer. That is an equation for a line (linear relationship).
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Esb said: Is following function linear? f(x) = k {y / (k -y)} where k is a constant, x and y are variable, k >y Click to expand... Okay, f(x) implies that we have a function written in terms of x. Yours is written in terms of y. There is no x on the RHS so there is a problem there right away. As to writing it in terms of a line, you can multiply both sides by k - y and solve for y as a function of f(x). But that won't tell you if it's linear. Either there's a typo or we need more information about what f(x) is. -Dan
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Well y = mx + c is not linear for a start. also your original expression is not even a function, as CaptainBlack has pointed out. If this is a set question please post is as set. If you are trying to construct something, please explain in words what you want to do.
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x and y are independent variables. What I meant by linear is a form like : y =mx + C I hope I am clear.
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Esb said: Is following function linear? f(x) = k {y / (k -y)} where k is a constant, x and y are variable, k >y Click to expand... What definition of linear are you supposed to be using? Also you have the variable x on one side and y on the other. Is that what you intend? Is y supposed to be a function of x?
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