Question

Please help with the questions.

Answer 1

Graph 1 ----->
`y \leq -3x-3`

Graph 2 ---->
`y<(2)/(3)x+1`

Graph 3 ---->
`y>2x-4`

Graph 4 ----->
`y \geq (x)/(3)+3`

Explanation:

Graph 1) we know that

The solution is the shaded area below (to the left) the solid line

The slope of the solid line is negative

The y-intercept of the solid line is (0,-3)

The x-intercept of the solid line is (-1,0)

The equation of the solid line is
`y=-3x-3`

therefore

The inequality is

`y \leq -3x-3`

Graph 2) we know that

The solution is the shaded area below the dashed line

The slope of the dashed line is positive

The y-intercept of the dashed line is (0,1)

The x-intercept of the dashed line is (-1.5,0)

The equation of the dashed line is
`y=(2)/(3)x+1`

therefore

The inequality is

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

Graph 3) we know that

The solution is the shaded area above the dashed line

The slope of the dashed line is positive

The y-intercept of the dashed line is (0,-4)

The x-intercept of the dashed line is (2,0)

The equation of the dashed line is
`y=2x-4`

therefore

The inequality is

`y>2x-4`

Graph 4) we know that

The solution is the shaded area above the solid line

The slope of the solid line is positive

The y-intercept of the solid line is (0,3)

The x-intercept of the solid line is (-9,0)

The equation of the solid line is
`y=(x)/(3)+3`

therefore

The inequality is

`y \geq (x)/(3)+3`