Given:
There are 4 equation representations are given.
To find:
The nonlinear equation.
Explanation:
A)
[tex]\begin{gathered} 3x-2y=7 \\ i.e)3x-2y-7=0 \end{gathered}[/tex]Which is of the linear form,
[tex]ax+by+c=0[/tex]B)
[tex]y=\frac{2}{3}x+8[/tex]Which is of the linear form,
[tex]y=mx+c[/tex]C)
Let us consider the two points.
[tex](5,0),(6,2)[/tex]Using the two-point formula,
[tex]\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}[/tex]Substituting the first point to verify the linear equation,
[tex]\begin{gathered} -4=2(3)-10 \\ -4=-4 \end{gathered}[/tex]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.