Question

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

Answer 1

C. y > 5/3x + 2

Answer 2

Option C.

Explanation:

Consider the below graph attached with this question.

The graph show the shaded area of

`y<(5)/(3)x+1`

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

`y=(5)/(3)x+1`

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
`y=(5)/(3)x+2` lies 1 unit up to the given related line.

`y<(5)/(3)x+1`

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

The given inequality and
`y<(5)/(3)x+1` have no shared solution.

Therefore, the correct option is C.