Write the linear inequality shown in the graph. the gray area represents the shaded region.

y < 4x - 2 is the inequality.

Step-by-step explanation:

In this question we will find the equation of the given line first.

This line passes through two points (0.5, 0) and (0, -2).

So the slope of this line will be =

slope =

         =

Y-intercept of the given dotted line is (-2)

Equation of the line will be y = 4x - 2

Now this line is in the dotted form so there is no equality, means it's a pure inequality.

So inequality may be y < 4x - 2 or y > 4x - 2

Now we will check the shaded area is for y < 4x - 2 or y > 4x - 2

Since gray area is on the right side of the inequality so we will take a point (2, 0) to check the inequality drawn on the graph.

0 < 4.(2) - 2

0 < 8 - 2

0 < 6 which is true.

For second inequality y > 4x - 2

0 > 4.(2) - 2

0 > 8 -2

0 > 6 which is not true.

Therefore, inequality representing the shaded area is y < 4x - 2