Determine if 7x2+y=5

Question

7
𝑥
2
+
𝑦
=
5
is a linear or nonlinear function.(1 point)
Responses

The graph of the function 7x2+y=5
7
𝑥
2
+
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
7
𝑥
2
+
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
7
𝑥
2
+
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
7
𝑥
2
+
𝑦
=
5
is a nonlinear function.
The function 7 x squared plus y equals 5 is a nonlinear function.

Answer 1

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

A linear function is typically in the form \( y = mx + b \), where \( m \) and \( b \) are constants, and \( x \) is raised only to the first power (i.e., no \( x^2 \), \( x^3 \), etc.).

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

• The term \( 7x^2 \) includes \( x^2 \), which indicates that the degree of \( x \) is 2.
• Therefore, the equation can be rearranged to express \( y \) in terms of \( x \):

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

Given that the highest power of \( x \) in the equation is 2 (quadratic), this means that the function is not linear.

Thus, the correct response is:

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