Question

Which linear inequality is represented by the graph?

1. y > 2/3x -2
2. y < 2/3x +2
3. y > 2/3x +1
4. y < 2/3x -1​

Answer 1

Option 4

Explanation:

It is clear that the line shown in the graph cuts to the y-axis at y = -1. Therefore, the equation that represents the line in the graph must be equal to -1 when x = 0.

The area that covers the inequality is below the line. Therefore, in this inequality the y-axis values must be less than the values of the linear function. That is to say:

`y <f (x)`.

The only option that meets these conditions is option 4. Therefore the inequality represented in the image is:
`y < (2)/(3)x -1`

Observe that:

If x = 0

Then

`y = (2)/(3)(0) -1\\\\y = -1.`