Determine if 7x2+y=5

Question

is a linear or nonlinear function.(1 point)
Responses

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.

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.

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

Answer 1

To determine whether the equation \( 7x^2 + y = 5 \) is a linear or nonlinear function, we should analyze the terms involved:

1. A linear function can be written in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. In a linear function, the variable \( x \) is raised only to the first power (i.e., \( x^1 \)), and there are no products or powers involving \( x \) other than \( x^1 \).

2. The given equation \( 7x^2 + y = 5 \) contains the term \( 7x^2 \), where \( x \) is raised to the second power (squared). This indicates a quadratic relationship rather than a linear one.

3. Therefore, the equation \( 7x^2 + y = 5 \) cannot be written in the form of a linear equation since it includes a squared term.

Based on this analysis, we can conclude:

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

So the correct response is:

The function \( 7x^2 + y = 5 \) is a nonlinear function. The graph of the function \( 7x^2 + y = 5 \) is not a straight line.