Answer:
[tex]5x-y\geq 1[/tex]
Step-by-step explanation:
We have been given graph of an inequality. We are asked to identify the inequality from the given graph.
First of all, we will find the equation of boundary line and then we will test any point to determine the shaded area.
Let us find slope of boundary line using point (1,4) and [tex](0,-1)[/tex] as:
[tex]m=\frac{4-(-1)}{1-0}=\frac{4+1}{1}=\frac{5}{1}=5[/tex]
Now, we will substitute coordinates of point (1,4) in point slope form as:
[tex]y-4=5(x-1)[/tex]
[tex]y-4=5x-5[/tex]
[tex]y-4+4=5x-5+4[/tex]
[tex]y=5x-1[/tex]
[tex]y-5x=5x-5x-1[/tex]
[tex]y-5x=-1[/tex]
Multiply both sides by negative 1:
[tex]-y+5x=1[/tex]
[tex]5x-y=1[/tex]
The equation of boundary line would be [tex]5x-y=1[/tex]. So one side of boundary line would be [tex]5x-y\leq 1[/tex] and other side would be [tex]5x-y\geq 1[/tex]
Now, we will test point (2,0) as it is shaded part of inequality.
[tex]5x-y\geq 1[/tex]
[tex]5(2)-0\geq 1[/tex]
[tex]10-0\geq 1[/tex]
[tex]10\geq 1[/tex]
Since point (2,0) holds the inequality true, therefore, our required inequality would be [tex]5x-y\geq 1[/tex].
