Question

Which system of linear inequalities is represented by the graph?

Answer 1

The system of inequalities is

`y\leq -(1)/(3)x+2`

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

Explanation:

step 1

Find the equation of the solid red line

Let

`A(0,2),B(3,1)`

Find the slope

`m=(1-2)/(3-0)=-1/3`

The equation of the line is

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

The solution of the inequality is the shaded area below the solid red line

therefore

The inequality is

`y\leq -(1)/(3)x+2`

step 2

Find the equation of the dashed blue line

Let

`A(0,3),B(3,5)`

Find the slope

`m=(5-3)/(3-0)=2/3`

The equation of the line is

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

The solution of the inequality is the shaded area above the dashed blue line

therefore

The inequality is

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

The system of inequalities is

`y\leq -(1)/(3)x+2`

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