Answer:
Option C.
Step-by-step explanation:
Consider the below graph attached with this question.
The graph show the shaded area of
[tex]y<\frac{5}{3}x+1[/tex]
We need to find a linear inequality that will not have a shared solution set with the graphed linear inequality.
It means the related of required inequality must be parallel to related line of given inequality.
The related equation is
[tex]y=\frac{5}{3}x+1[/tex]
Here, the slope of the line is 5/3.
Slope of two parallel line are same. So, the slope of required related line must be 5/3.
The related line [tex]y=\frac{5}{3}x+2[/tex] lies 1 unit up to the given related line.
[tex]y<\frac{5}{3}x+1[/tex]
Here, the sign of inequality is >, it means the shaded region lies above the line.
The given inequality and [tex]y<\frac{5}{3}x+1[/tex] have no shared solution.
Therefore, the correct option is C.
