What is the Independent Variable What is the Independent Variable In order to solve the mathematical equations, we need to use the Independent and dependent variable for keeping the track on what’s going on and what if analysis is done with the help of using the variables of the given equations. A dependent variable is the one whose value depends upon the change of the value of another variable. Now let’s see What is the Independent Variable? A variable which does not depend upon the value of the variable is called Independent variable. Let us take an example : X= y + 1. Here as the value of y changes, the value of x also changes with it. In this we find that the value of x is dependent on the value of Y. So we conclude that x is a dependent variable and y is independent variable. A variable in the given equation will always have its value freely taken without taking the value of other variable. Let us consider an equation say Y= 4x-3, here we observe that the value of y depends upon the change of value of x in the given equation. So we come to a conclusion that the value of y depends upon the change chosen value of x.
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Thus we conclude that the variable which can be assigned to any equation without any restrictions implemented by any another variable and has any permissible value in the equation is called an independent variable. An independent variable helps us in keeping the track on the Variable. Here we have some set of equations which have two variables. We will check which among these are independent variables and which among these are dependent variables. 1. 3x + 5 = y, here we find that as the value of x changes, the value of y also changes. So we conclude that the value of x is independent of y. The value of y depend on the value x, which means that if the value of x increases, the value of y also increases. Similarly the value of y decreases, if the value of x decreases. So we conclude that the variable x is independent and the variable y is dependent on the value of x. 2. If we take the equation a + 3b = c. Here the value of c depends on the value of a and b. But we observe that the value of a and b do not depend upon the value of c. So we can say that the variables a and b are independent and the variable c is dependent on variable a and b 3. Let see another equation x^2 – y^2 = z^2. Here in this equation, we find, the more we increase the value of x, the value of z also increases, on the other hand the more we increase the value of y, the value of z decreases. As we find that y has a negative relation with the variable z. So here the variable x and y are independent and the variable z is a dependent variable.
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Example 1 : Solve the equation 5x+4y +8 =0 Fine the coordinate of vertexes of lines and the x axis in the polynomial. Solution: Given 5x+4y +8 =0 Substitute x = 0 in the given equation we get, 5(0) +4y +8=0 4y+8=0 Subtract 8 on both sides we get , 4y + 8 - 8 = 0 - 8 4y = -8
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