Is y=20−bx2 a linear equation? Linear equations are all equations where the highest degree of the expression is 1 but l want to know whether there are other forms of linear equations. Consider y=20−bx2 where y is a function of x2. Will this also be a linear equation even though it is a second degree expression? Does it make a difference if I say y is a function of x2 instead of x.

Question

Is y=20−bx2 a linear equation?  Linear equations are all equations where the highest degree of the expression is 1 but l want to know whether there are other forms of linear equations.  Consider y=20−bx2 where y is a function of x2. Will this also be a linear equation even though it is a second degree expression? Does it make a difference if I say y is a function of x2 instead of x.

Vasquez · Accepted Answer

It is a linear equation with respect to x2. It is a non-linear(quadratic) with respect to x. You cannot define linearity without defining what element you choose to see the variation. Even y=sin⁡(x) is linear with respect to sin⁡(x), or y=x is non linear with respect to x The word itself refers to the graph of the function with respect to the variable you wish to see. Conventionally, unless specifically mentioned, it is assumed that the function is with respect to x. So, if you give y=20−x2, one would say that it is a quadratic equation. However, the correct statement should be - it is a quadratic equation with respect to x.

Is y=20-bx^{2} a linear equation? Linear equations are all equations where the highest deg

Answered question

Answer & Explanation

New Questions in Algebra I