Determine if 7x2+y=5 is a linear or nonlinear function.(1 point)

Question

Responses

The graph of the function 7x2+y=5 is not a straight line.
The graph of the function 7 x squared plus y equals 5 is not a straight line.

The function 7x2+y=5 is a linear function.
The function 7 x squared plus y equals 5 is a linear function.

The function 7x2+y=5 is a nonlinear function.
The function 7 x squared plus y equals 5 is a nonlinear function.

There is not enough information to determine if 7x2+y=5 is a linear or nonlinear function.
There is not enough information to determine if 7 x squared plus y equals 5 is a linear or nonlinear function.

Answer 1

To determine if the equation \(7x^2 + y = 5\) represents a linear or nonlinear function, we need to analyze the equation.

In general, a linear function can be written in the form \(y = mx + b\), where \(m\) and \(b\) are constants. A key characteristic of linear functions is that they do not contain any variables raised to a power greater than 1 (e.g., \(x^2\), \(x^3\), etc.).

In the equation \(7x^2 + y = 5\):

• The term \(7x^2\) contains \(x\) raised to the power of 2, which indicates that this is not a linear equation.

To convert the equation into the standard form, we can isolate \(y\):

\[ y = 5 - 7x^2 \]

Since \(x\) is squared, this shows that the relationship between \(x\) and \(y\) is not linear.

Thus, we conclude that:

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