To determine if the equation \( 6x^2 + y = 7 \) is a linear or nonlinear function, we need to analyze the degree of the terms involved.
A linear function can be written in the form \( y = mx + b \), where \( m \) and \( b \) are constants, and the highest power of the variable \( x \) is 1.
In the given equation \( 6x^2 + y = 7 \):
- The term \( 6x^2 \) has \( x \) raised to the power of 2, which is higher than 1.
- The term \( y \) is treated as a variable that represents output, and its degree is considered to be 1 when it is isolated.
To rewrite the equation in a function form, we can isolate \( y \):
\[ y = 7 - 6x^2 \]
Now, we see that the function involves \( x^2 \), which indicates that it is a quadratic term (degree 2).
Thus, since the highest power of \( x \) in the equation is 2, the equation represents a nonlinear function.
Therefore, the equation \( 6x^2 + y = 7 \) is a nonlinear function.