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

Answer: $y<4x-2$

Step-by-step 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:-

$(y-(-2))=\frac{2-(-2)}{1-0}(x-0)\\\Rightarrow\ (y+2)=\frac{4}{1}x\\\Rightarrow\ y=4x-2$..(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 :-

$y<4x-2$

Answer 2

Answer:

D: y < 4x – 2

Step-by-step 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