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,
[tex]y - 0 = \frac{4-0}{0-1} (x-1)[/tex]
⇒ [tex]y = \frac{4}{-1} (x-1)[/tex]
⇒ [tex]- y = 4(x-1)[/tex]
⇒ [tex]-y = 4x - 4[/tex]
⇒ [tex]4x - 4 + y = 0[/tex]
⇒ [tex]4x + y = 4[/tex]
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.
