Question

Need this ASAP please help!#2

Answer 1

The correct option is 3.

Explanation:

From the given graph it is noticed that the related line passing through the point (-3,1) and (0,3).

If a line passing through two points, then the equation of line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

The equation of related line is

`y-1=(3-1)/(0-(-3))(x-(-3))`

`y-1=(2)/(3)(x+3)`

`y-1=(2)/(3)(x)+2`

Add 1 on both the sides.

`y=(2)/(3)(x)+2+1`

`y=(2)/(3)(x)+3`

The equation of related line is
`y=(2)/(3)(x)+3`.

The related line is a dotted line, it means the point on the line does not included in the solution set.

The shaded region is above the line so the sign of inequity is >.

The required inequality is

`y>(2)/(3)(x)+3`

Therefore option 3 is correct.