Question

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

Answer 1

Answer:  4x + y ≥ 4

Step-by-step explanation:

By the given graph,

The x-intercept of the line is , (1,0)

And, the y-intercept of the line is, (0,4)

Thus, the relation equation of the inequality,

$y - 0 = \frac{4-0}{0-1} (x-1)$

⇒  $y = \frac{4}{-1} (x-1)$

⇒ $- y = 4(x-1)$

⇒ $-y = 4x - 4$

⇒  $4x - 4 + y = 0$

⇒ $4x + y = 4$

Again, by the graph the inequality does not contain the origin.

Therefore, the possible inequalities are, 4x + y > 4 and 4x + y ≥ 4

Also, the line of related equation in the graph is a solid line,

⇒ The inequalities must hold the sign ≥.

Thus, the required inequality that shown in the given graph is,

4x + y ≥ 4

⇒ Fourth option is correct.

Answer 2

4x + y > 4 Should be you're answer.....