Which linear inequality will not have a shared solution set with the graphed linear inequality? a. y < 5/3x – 2 b. y < -5/3x + 1 c. y > 5/3x + 2 d. y > -5/3x + 2

Option C.

Step-by-step explanation:

Consider the below graph attached with this question.

The graph show the shaded area of

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

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 lies 1 unit up to the given related line.

Here, the sign of inequality is >, it means the shaded region lies above the line.

The given inequality and have no shared solution.

Therefore, the correct option is C.