Question
Determine if 7x2+y=5
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.
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.
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.
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.
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.
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.
Answers
GPT-4o mini
To determine whether the equation \(7x^2 + y = 5\) is a linear or nonlinear function, we should examine the terms involved.
A linear function is typically of the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. In contrast, a nonlinear function might have terms that are squared, cubed, or other higher powers.
In the equation \(7x^2 + y = 5\), the term \(7x^2\) involves \(x^2\), which indicates that this equation does not represent a straight line.
To express \(y\) explicitly, we can rearrange the equation:
\[y = 5 - 7x^2.\]
The presence of the \(x^2\) term confirms that this function is nonlinear.
Thus, the correct response is:
**The function 7x^2 + y = 5 is a nonlinear function.**
A linear function is typically of the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. In contrast, a nonlinear function might have terms that are squared, cubed, or other higher powers.
In the equation \(7x^2 + y = 5\), the term \(7x^2\) involves \(x^2\), which indicates that this equation does not represent a straight line.
To express \(y\) explicitly, we can rearrange the equation:
\[y = 5 - 7x^2.\]
The presence of the \(x^2\) term confirms that this function is nonlinear.
Thus, the correct response is:
**The function 7x^2 + y = 5 is a nonlinear function.**