Question

Write an inequality and that represents the graph.

Answer 1

Part 16)
`y\leq -x+2`

Part 17)
`y>(1)/(3)x-1`

Explanation:

Part 16) we know that

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

The slope of the solid line is negative

The y-intercept of the solid line is the point (0,2)

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

The slope of the solid line is

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

The linear equation of the solid line in slope intercept form is

`y=-x+2`

therefore

The inequality that represent the graph is

`y\leq -x+2`

Part 17) we know that

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

The slope of the dashed line is positive

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

The x-intercept of the dashed line is the point (3,0)

The slope of the dashed line is

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

The linear equation of the dashed line in slope intercept form is

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

therefore

The inequality that represent the graph is

`y>(1)/(3)x-1`