Question

Choose the linear inequality that describes the graph. The gray area represents the shaded region.

A: y ≤ –4x – 2

B: y > –4x – 2

C: y ≥ –4x – 2

D: y < 4x – 2

Answer 1

D: y < 4x – 2

Explanation:

The line here is dashed. This means that the inequality is not equal to; it is strictly less than or greater than.

Since the section below the line is shaded, this is a "less than" inequality.

The y-intercept of the dashed line is -2 and the slope goes up 4 and over 1; this makes the line y = 4x - 2.

This gives us the inequality

y < 4x - 2

Answer 2

Answer:
`y<4x-2`

Explanation:

By the given graph,

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

and the line is passing through point (1,2)

The equation of line passing through points (0,-2) and (1,2) is given by:-

`(y-(-2))=(2-(-2))/(1-0)(x-0)\\\Rightarrow\ (y+2)=(4)/(1)x\\\Rightarrow\ y=4x-2`..(1)

Since the line is dashed, which means the shaded region does not include the given line.

Also it is shading above the line, means "greater than" or < []

By replacing "= sign" with < , the required inequality for the given graph is :-

`y<4x-2`