Determine if 7x^2 +y=5 is a linear function or nonlinear

Answer 1

To determine if the function \(7x^2 + y = 5\) is linear or nonlinear, we need to understand what constitutes a linear function.

A linear function has the following general form:
\[ ax + by = c \]
where \(a\), \(b\), and \(c\) are constants, \(x\) and \(y\) are variables, and there are no exponents greater than 1 on the variables. Linear functions represent straight lines in a coordinate system.

In your function, \(7x^2 + y = 5\), the term \(7x^2\) is a quadratic term because it involves \(x\) raised to the power of 2. The presence of this quadratic term means that the function is not linear. Linear functions do not include quadratic (second degree) or higher degree terms.

Thus, \(7x^2 + y = 5\) is a **nonlinear** function.