Question

What system of linear inequalities is shown in the graph?

Enter your answers in the boxes.

Answer 1

y<-3x+1
y≥
`(1)/(2) x-1`

Answer 2

For dotted line y < -3x + 1.

For solid line : y ≥
`(1x)/(2)-1`.

Explanation:

Given : Graph.

To find: What system of linear inequalities,

Solution: We have given a graph.

We can see the graph having two line one is dotted and another is solid line.

By the slope intercept form of equation : y = mx + b

Where, m = slope

b ( where the line intercept at y axis) = y intercept.

For dotted line : we use the less than sign for dotted line and shaded down.

We can see slope of dotted line is -3 and it cut at 1 on y axis.

m = -3 , b = 1

Then equation become

y < -3x + 1.

For solid line :

we use the greater than or equal to sign for solid line and shaded up.

We can see slope of dotted line is 1/2 and it cut at -1 on y axis.

m = -3 , b = 1

Then equation become

y ≥
`(1x)/(2)-1`.

Therefore, For dotted line y < -3x + 1.

For solid line : y ≥
`(1x)/(2)-1`.