Question

Which function is nonlinear?Which equation represents a nonlinear function? (Let me know if you can’t read the possible answers for the equation and I will send them)

Answer 1

Given:

There are 4 equation representations are given.

To find:

The nonlinear equation.

Explanation:

A)

$\begin{gathered} 3x-2y=7 \\ i.e)3x-2y-7=0 \end{gathered}$

Which is of the linear form,

$ax+by+c=0$

B)

$y=\frac{2}{3}x+8$

Which is of the linear form,

$y=mx+c$

C)

Let us consider the two points.

$(5,0),(6,2)$

Using the two-point formula,

$\begin{gathered} \frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1} \\ \frac{y-0}{2-0}=\frac{x-5}{6-5} \\ \frac{y}{2}=\frac{x-5}{1} \\ y=2x-10 \end{gathered}$

Substituting the first point to verify the linear equation,

$\begin{gathered} -4=2(3)-10 \\ -4=-4 \end{gathered}$

Therefore, the linear equation is satisfied for all 4 points.

Thus, options A, B, and C are linear equation.

So, the nonlinear equation must be given options D.

Final answer:

The correct option is D.